The Christian Jesus is different from the Muslim Jesus in a very different sense.

Islamic Jesus: Human-only-by-nature

In Islam, Jesus is merely one of prophets of God who is only one person.

"Christ, the son of Mary, was no more than a messenger; many were the messengers that passed away before him. His mother was a woman of truth. They had both to eat their (daily) food. See how God makes His signs clear to them; yet see in what ways they are deluded away from the truth!" (5:75).

Christianity's Jesus: God in the flesh

In Christianity, Jesus is the Pre-existent Christ who is of same nature with God. He's the eternal Son, Wisdom and Power of God, the Son who is eternally begotten from the Father.He's the active agent of creation. The Christian Scriptures are clear: Jesus is God himself who sends prophets:

I begot you from my womb, before the morning star ( Psalm 110:3 LXX)

In the beginning was the Word, and the Word was with God, and the Word was God ( John 1:1)

The Son...by whom he created the universe ( Hebrews 1:2)

Therefore, behold, I am sending you prophets and wise men and scribes; some of them you will kill and crucify, and some of them you will scourge in your synagogues, and persecute from city to city,( Matthew 23:34).

Christianity, as we all already know, tells the story of Jesus as,

• him being God,
• and/or son of God.
• with miracles,
• crucified and died for sins,
• resurrected,
• will come back again.

However there are different forms of Christianity, Unitarian, that is to believe Jesus was a prophet sent by God.

What Muslims do not agree and what they suggest:

• God is exalted and He has no companions, partners, parts, equals, opposites, sons or anything against absolute Unity and Uniqueness. Therefore, not only Jesus, but anything cannot be attributed to Him as a son.
• Jesus was a prophet, born fatherless, showing miracles, but not God, or God-incarnate, because Muslims believe God cannot be in any state confined, needy or of slightest weakness. God to eat, sleep, have flesh and be in any state that is a part of the creation or depending on the creation is impossible, illogical and even thinking of it is an insult to His greatness.
• Jesus was never crucified, because they believe Allah would save his beloved servant from such a state of torture in the hands of his enemies. And indeed, Allah saved him, and he is still alive.
• Since Jesus was never crucified, he was never resurrected, people saw him after the Crucifixion, because he was never dead at all! He is still alive.
• Jesus will come back, but he will not be with Christians. He will be with Muslims and will "break the Cross" and "kill the swine". He will die a humanly death.
• No one needs to die for others' sins. There is no original sin and God just forgives, does not need any reason, He may even forgive sins that are not repented because He is "All-Forgiving".

From its original source, the Quran, quotations on the matter:

A part, pretty much explains what Muslims do not agree from all aspects:

42.And [mention] when the angels said, "O Mary, indeed Allah has chosen you and purified you and chosen you above the women of the worlds.
43.O Mary, be devoutly obedient to your Lord and prostrate and bow with those who bow [in prayer]."
44. That is from the news of the unseen which We reveal to you, [O Muhammad]. And you were not with them when they cast their pens as to which of them should be responsible for Mary. Nor were you with them when they disputed.
45.[And mention] when the angels said, "O Mary, indeed Allah gives you good tidings of a word from Him, whose name will be the Messiah, Jesus, the son of Mary - distinguished in this world and the Hereafter and among those brought near [to Allah ].
46.He will speak to the people in the cradle and in maturity and will be of the righteous."
47.She said, "My Lord, how will I have a child when no man has touched me?" [The angel] said, "Such is Allah ; He creates what He wills. When He decrees a matter, He only says to it, 'Be,' and it is.
48.And He will teach him writing and wisdom and the Torah and the Gospel
49.And [make him] a messenger to the Children of Israel, [who will say], 'Indeed I have come to you with a sign from your Lord in that I design for you from clay [that which is] like the form of a bird, then I breathe into it and it becomes a bird by permission of Allah . And I cure the blind and the leper, and I give life to the dead - by permission of Allah . And I inform you of what you eat and what you store in your houses. Indeed in that is a sign for you, if you are believers.
50.And [I have come] confirming what was before me of the Torah and to make lawful for you some of what was forbidden to you. And I have come to you with a sign from your Lord, so fear Allah and obey me.
51.Indeed, Allah is my Lord and your Lord, so worship Him. That is the straight path."
52.But when Jesus felt [persistence in] disbelief from them, he said, "Who are my supporters for [the cause of] Allah ?" The disciples said," We are supporters for Allah . We have believed in Allah and testify that we are Muslims [submitting to Him].
53.Our Lord, we have believed in what You revealed and have followed the messenger Jesus, so register us among the witnesses [to truth]."
54.And the disbelievers planned, but Allah planned. And Allah is the best of planners.
55.[Mention] when Allah said, "O Jesus, indeed I will take you and raise you to Myself and purify you from those who disbelieve and make those who follow you [in submission to Allah alone] superior to those who disbelieve until the Day of Resurrection. Then to Me is your return, and I will judge between you concerning that in which you used to differ.
56.And as for those who disbelieved, I will punish them with a severe punishment in this world and the Hereafter, and they will have no helpers."
57.But as for those who believed and did righteous deeds, He will give them in full their rewards, and Allah does not like the wrongdoers.
58.This is what We recite to you, [O Muhammad], of [Our] verses and the precise [and wise] message.
59.Indeed, the example of Jesus to Allah is like that of Adam. He created Him from dust; then He said to him, "Be," and he was.
60.The truth is from your Lord, so do not be among the doubters.
61.Then whoever argues with you about it after [this] knowledge has come to you - say, "Come, let us call our sons and your sons, our women and your women, ourselves and yourselves, then supplicate earnestly [together] and invoke the curse of Allah upon the liars [among us]."
62.Indeed, this is the true narration. And there is no deity except Allah . And indeed, Allah is the Exalted in Might, the Wise.
63.But if they turn away, then indeed - Allah is Knowing of the corrupters.
64.Say, "O People of the Scripture, come to a word that is equitable between us and you - that we will not worship except Allah and not associate anything with Him and not take one another as lords instead of Allah ." But if they turn away, then say, "Bear witness that we are Muslims [submitting to Him]."
65.O People of the Scripture, why do you argue about Abraham while the Torah and the Gospel were not revealed until after him? Then will you not reason?
66.Here you are - those who have argued about that of which you have [some] knowledge, but why do you argue about that of which you have no knowledge? And Allah knows, while you know not.
67.Abraham was neither a Jew nor a Christian, but he was one inclining toward truth, a Muslim [submitting to Allah ]. And he was not of the polytheists. http://quran.com/3/42-67

Islam's basic stance on Jesus:

According to Islam,

1. Jesus was born fatherless, and with miracles.

16.​ And mention, [O Muhammad], in the Book [the story of] Mary, when she withdrew from her family to a place toward the east.
17. And she took, in seclusion from them, a screen. Then We sent to her Our Angel, and he represented himself to her as a well-proportioned man.
18. She said, "Indeed, I seek refuge in the Most Merciful from you, [so leave me], if you should be fearing of Allah ."
19. He said, "I am only the messenger of your Lord to give you [news of] a pure boy."
20. She said, "How can I have a boy while no man has touched me and I have not been unchaste?"
21. He said, "Thus [it will be]; your Lord says, 'It is easy for Me, and We will make him a sign to the people and a mercy from Us. And it is a matter [already] decreed.' "
22. So she conceived him, and she withdrew with him to a remote place.
23. And the pains of childbirth drove her to the trunk of a palm tree. She said, "Oh, I wish I had died before this and was in oblivion, forgotten."
24. But he called her from below her, "Do not grieve; your Lord has provided beneath you a stream.
25. And shake toward you the trunk of the palm tree; it will drop upon you ripe, fresh dates.
26. So eat and drink and be contented. And if you see from among humanity anyone, say, 'Indeed, I have vowed to the Most Merciful abstention, so I will not speak today to [any] man.' "​
​27.Then she brought him to her people, carrying him. They said, "O Mary, you have certainly done a thing unprecedented.
28.O sister of Aaron, your father was not a man of evil, nor was your mother unchaste."
29.So she pointed to him. They said, "How can we speak to one who is in the cradle a child?"
30.[Jesus] said, "Indeed, I am the servant of Allah . He has given me the Scripture and made me a prophet.
31.And He has made me blessed wherever I am and has enjoined upon me prayer and zakah as long as I remain alive
32.And [made me] dutiful to my mother, and He has not made me a wretched tyrant.
33.And peace is on me the day I was born and the day I will die and the day I am raised alive."
34.That is Jesus, the son of Mary - the word of truth about which they are in dispute.
35.It is not [befitting] for Allah to take a son; exalted is He! When He decrees an affair, He only says to it, "Be," and it is.
36.[Jesus said], "And indeed, Allah is my Lord and your Lord, so worship Him. That is a straight path."​ http://quran.com/19

2. Jesus is the Messiah.

[And mention] when the angels said, "O Mary, indeed Allah gives you good tidings of a word from Him, whose name will be the Messiah, Jesus, the son of Mary - distinguished in this world and the Hereafter and among those brought near [to Allah ]. http://quran.com/3/45

3. Jesus is the Word of Allah.

O People of the Scripture, do not commit excess in your religion or say about Allah except the truth. The Messiah, Jesus, the son of Mary, was but a messenger of Allah and His word which He directed to Mary and a soul [created at a command] from Him. So believe in Allah and His messengers. And do not say, "Three"; desist - it is better for you. Indeed, Allah is but one God. Exalted is He above having a son. To Him belongs whatever is in the heavens and whatever is on the earth. And sufficient is Allah as Disposer of affairs. http://quran.com/4/171

4. Jesus is a messenger, a human-being and a servant of Allah.

The Messiah, son of Mary, was not but a messenger; [other] messengers have passed on before him. And his mother was a supporter of truth. They both used to eat food. Look how We make clear to them the signs; then look how they are deluded. http://quran.com/5/75

Never would the Messiah disdain to be a servant of Allah , nor would the angels near [to Him]. And whoever disdains His worship and is arrogant - He will gather them to Himself all together. http://quran.com/4/172

And We did certainly give Moses the Torah and followed up after him with messengers. And We gave Jesus, the son of Mary, clear proofs and supported him with the Pure Spirit. But is it [not] that every time a messenger came to you, [O Children of Israel], with what your souls did not desire, you were arrogant? And a party [of messengers] you denied and another party you killed. http://quran.com/2/87

5. Jesus is one of the distinguished prophets.

Those messengers - some of them We caused to exceed others. Among them were those to whom Allah spoke, and He raised some of them in degree. And We gave Jesus, the Son of Mary, clear proofs, and We supported him with the Pure Spirit. If Allah had willed, those [generations] succeeding them would not have fought each other after the clear proofs had come to them. But they differed, and some of them believed and some of them disbelieved. And if Allah had willed, they would not have fought each other, but Allah does what He intends. http://quran.com/2/253

6. Jesus showed tremendous miracles such as breathing life to clay and raising the dead.

[The Day] when Allah will say, "O Jesus, Son of Mary, remember My favor upon you and upon your mother when I supported you with the Pure Spirit and you spoke to the people in the cradle and in maturity; and [remember] when I taught you writing and wisdom and the Torah and the Gospel; and when you designed from clay [what was] like the form of a bird with My permission, then you breathed into it, and it became a bird with My permission; and you healed the blind and the leper with My permission; and when you brought forth the dead with My permission; and when I restrained the Children of Israel from [killing] you when you came to them with clear proofs and those who disbelieved among them said, "This is not but obvious magic." http://quran.com/5/110

7. Jesus was never crucified and he is still alive and will come back.

157.And [We cursed them for] their saying, "Indeed, we have killed the Messiah, Jesus, the son of Mary, the messenger of Allah ." And they did not kill him, nor did they crucify him; but [another] was made to resemble him to them. And indeed, those who differ over it are in doubt about it. They have no knowledge of it except the following of assumption. And they did not kill him, for certain.
158. Rather, Allah raised him to Himself. And ever is Allah Exalted in Might and Wise. http://quran.com/4/157

[Mention] when Allah said, "O Jesus, indeed I will take you and raise you to Myself and purify you from those who disbelieve and make those who follow you [in submission to Allah alone] superior to those who disbelieve until the Day of Resurrection. Then to Me is your return, and I will judge between you concerning that in which you used to differ. http://quran.com/3/55

8. Jesus is definitely neither the son of God, nor God.

Indeed, the example of Jesus to Allah is like that of Adam. He created Him from dust; then He said to him, "Be," and he was. http://quran.com/3/59

30.The Jews say, "Ezra is the son of Allah "; and the Christians say, "The Messiah is the son of Allah ." That is their statement from their mouths; they imitate the saying of those who disbelieved [before them]. May Allah destroy them; how are they deluded? 31.They have taken their scholars and monks as lords besides Allah , and [also] the Messiah, the son of Mary. And they were not commanded except to worship one God; there is no deity except Him. Exalted is He above whatever they associate with Him. http://quran.com/9/30-31

They have certainly disbelieved who say that Allah is Christ, the son of Mary. Say, "Then who could prevent Allah at all if He had intended to destroy Christ, the son of Mary, or his mother or everyone on the earth?" And to Allah belongs the dominion of the heavens and the earth and whatever is between them. He creates what He wills, and Allah is over all things competent. http://quran.com/5/17

They have certainly disbelieved who say, "Allah is the Messiah, the son of Mary" while the Messiah has said, "O Children of Israel, worship Allah , my Lord and your Lord." Indeed, he who associates others with Allah - Allah has forbidden him Paradise, and his refuge is the Fire. And there are not for the wrongdoers any helpers. http://quran.com/5/72

88.And they say, "The Most Merciful has taken [for Himself] a son."
89.You have done an atrocious thing.
90.The heavens almost rupture therefrom and the earth splits open and the mountains collapse in devastation.
91.That they attribute to the Most Merciful a son.
92.And it is not appropriate for the Most Merciful that He should take a son.
93.There is no one in the heavens and earth but that he comes to the Most Merciful as a servant.
94.He has enumerated them and counted them a [full] counting.
95.And all of them are coming to Him on the Day of Resurrection alone.
96.Indeed, those who have believed and done righteous deeds - the Most Merciful will appoint for them affection.
97.So, [O Muhammad], We have only made Qur'an easy in the Arabic language that you may give good tidings thereby to the righteous and warn thereby a hostile people.
98.And how many have We destroyed before them of generations? Do you perceive of them anyone or hear from them a sound? http://quran.com/19/88-98

Some opinions of Islam on Jesus which is possibly similar to christian belief-

• Born from a virgin mother.
• Was a true prophet, sent to the children of israel.
• Was the promised messiah/christ the children of Israel were waiting for.
• Preached true word of one God, forbade idolatry.
• Was able to talk from the first day of his life and performed other miracles.
• Came with new ruling for children of Israel from God, including some exemption of previous rules.
• Will come again on earth to fight the false messiah/anti christ.
• Will rule the world as a king with justice (after Mahdi).

Some differing points may be-

• Being Son of God
• Being part of God
• Removing all the sins from the believers

Islam accepts Jesus as a prophet. A man of God so to speak. They also believe he was born of a virgin and did miracles, but take the Gnostic Gospels take on his crucifixion and somehow think that it was just a big hoax and some even think that it was Judas who died on the cross.

It is one of the greatest ironies of Islam that the one thing they differ from Christians about Jesus is the thing that is most uncontroversial about him. That he died on the cross. It is the one thing that almost all of the New Testament scholars believe is true.

Even the some of the radical New Testament Historians are willing to believe that he died on the cross (although the differ on other issues regarding him.

Source 1, Source 2

Why not take a look at the same question from the Muslim perspective, which is actually very informative:

How does Muslim teaching on the person of Jesus differ from that of Christian teaching?

UPDATE:

Muslims believe Jesus (Isa Masih):

• is the Word of God, Spirit of God and other similar titles that are present in Christianity also, but they believe these attribute are not necessarily unique to Jesus
• was one of the 5 great prophets (Noah, Abraham, Moses, JESUS and Muhammad)
• is a creation of God not creator and certainly not a son of God (as opposed to the Christian belief)
• was the messiah but does not save through dying on the cross
• will come again, same as Christians but for a different purpose and in a different way

Here are the differences:

Christianity

1. Jesus is God.
2. Jesus died and rose again to save the world from all their sins.
3. Jesus is the way to eternity in heaven.

Islam

1. Jesus is not God, he was just a good prophet.
2. Jesus did not rise again.
   a. He was never crucified, nor would God ever let one of his prophets die in such a fashion.
3. Jesus does not save us. Instead, our works save us.

I hope this answers your question.

Source: The Dark Side of Islam by R. C. Sproul, Abdul Saleeb