Why do Christians have different books in their Bible?

Most of the books of the Bible were written by different people. An estimated 40 authors wrote the 70 or so books that various Christians accept as "the Bible". Most of these authors wrote independently from each other; if they were contemporaries, they typically did not confer with each other. If they were separated by time, the latter typically did not write with an apparent expectation that what he wrote would be considered scripture even though the former was during his time.

What you are referring to is the Bible Canon. A canon is

a regulation or dogma decreed by a church council.
Merriam Webster Dictionary

Basically, many Christians already followed many or even all of these books as scripture, then through councils called by early church leaders, a canon was set, decreeing them as scripture, indeed. These councils also set out to decree some theologies as Christian dogma and others as not Christian dogma. More rarely, some books were explicitly decreed not canon. These typically go by the names Apocrypha/Deuterocanonical books, Gnostic Gospels, or Pseudepigrapha. These books were accepted by fringe groups and rejected by the larger majority. This and among real issues (some teach dissonant doctrine) is why they were not included in the Biblical Canon. Most of them were just ignored or so fringe they were unheard of among the council members. ¹

Today, there are three primary canons: The Catholic bible canon, the Protestant bible canon, and the Eastern/Greek Orthodox bible canon. In general, there was only the Catholic bible canon until Martin Luther started the Protestant Reformation in the 16th century. Martin Luther had many ideas that radically changed the face of Christianity, including views that led to the formation of the Protestant bible canon, which essentially removed 7 books from the Catholic bible canon and a few portions of some other books, but added nothing. Those books/portions present in the Catholic bible, but not in the Protestant bible are:

• Tobit
• Judith
• Additions to Esther (Vulgate Esther 10:4–16:24)
• Wisdom (also called the Wisdom of Solomon)
• Sirach (also called Ecclesiasticus)
• Baruch, including the Letter of Jeremiah (Additions to Jeremiah in the Septuagint)
• Additions to Daniel:
  • Prayer of Azariah and Song of the Three Holy Children (Vulgate Daniel 3:24–90)
  • Susanna (Vulgate Daniel 13, Septuagint prologue)
  • Bel and the Dragon (Vulgate Daniel 14, Septuagint epilogue)
• 1 Maccabees
• 2 Maccabees
  ^{See "Deuterocanonical books - Wikipedia" for more information}

The following table helps compare all the major canons. See the footnotes for a comprehensive list of all the books.

^Source

There are a few other canons in some much smaller segments of the Christian population, but those are typically very small in their number of adherents. For example, the Church of Ethiopia has a few more books in their canon than the Catholic canon. ²

Summary

The books accepted by any Christian group is called a canon. There are three major canons, one for the Catholics, one for the Eastern Orthodox, and one for the Protestants. The canon was decreed as "scripture" by early church councils, mostly based on the widespread use of these books. Over the centuries, there has been plenty of debate on the actual authenticity of these books, from both historical and theological perspectives. To many theologians and historians, the authenticity of any given book is a matter of independent study of those individual books, and opinions tend to vary widely among theologians, but tend to fall one way or the other among historians.

Sources and further information

1. Biblical Canon - Wikipedia
2. Development of the Christian biblical canon - Wikipedia

3. Books of the Bible - Wikipedia

   Other Questions on Christianity Stack Exchange

4. Resources to learn about Bible canonization

5. How long did it take to form the Biblical canon?
6. When was the Biblical canon formalised?
7. How were the books of the New Testament chosen?
8. What writings are held as "biblical canon" by Swedenborgians? (example of a small group with a unique and heavily trimmed canon)
9. How many 'Books' never made it to the Bible (Old and New Testament)?
10. When did the idea of a scriptural "canon" originate?

Footnotes:

1. Disclaimer: This is a gross simplification of a long and complicated topic rife with historical debate that goes back to the second century and continues today. For example, this brief synopsis implies that Martin Luther is responsible for all of it, but that is far from the case. The differences between the Eastern Orthodox and the Roman Catholic churches manifested a thousand years before Luther and came to a head in the 11th century with the Great Schism. Further complicating the issue, what Christians call the Old Testament was part of the Hebrew/Jewish Bible canon which has its own long history of development that for the most part, Christianity just inherited. If you want to have a solid grasp on what actually happened, you will need to read no fewer than 200 pages on the subject.

2. There are, of course, some modern churches that claim the Christian title that have wildly different canons. The LDS church, for example, accepts the Protestant Canon, in addition to the many books found in the Book of Mormon, Doctrines and Covenants, and the Pearl of Great Price. There are no other Christians that accept these books as scripture.

3. Comprehensive list of all the books of "the bible" (Source):

   Hebrew Bible

   All extant manuscripts of the following texts:

   Torah (Books of Moses)

   • Genesis
   • Exodus
   • Leviticus
   • Numbers
   • Deuteronomy

   The Samaritan Pentateuch is also included.

   Nevi'im (Prophets)

   • Joshua
   • Judges
   • Kingdoms (I - IV)
     • Samuel (I & II)
     • Kings (I & II)
   • Isaiah
   • Jeremiah
   • Ezekiel
   • Twelve Prophets
     • Hosea
     • Joel
     • Amos
     • Obadiah
     • Jonah
     • Micah
     • Nahum
     • Habakkuk
     • Zephaniah
     • Haggai
     • Zechariah
     • Malachi

   Kethuvim (Writings)

   • Psalms (including manuscripts containing 151 psalms)
   • Proverbs
   • Job
   • The Song of Songs
   • Ruth
   • Lamentations
   • Ecclesiastes
   • Esther (including manuscripts containing The Additions)
   • Daniel (including manuscripts containing Susanna, Bel and the Serpent/Dragon, and/or the Hymn of the Three Youths)
   • Ezra-Nehemiah / Esdras (I & II)
   • Chronicles / Paraleipomenon (I & II, including manuscripts containing the Prayer of Manasseh)

   Care should be taken to clearly refer to relevant sections of the Hebrew Bible as chapter and verse sections as well as the order of content is not consistent between many translations, manuscripts, and critical texts.

   ---

   Apocrypha

   All extant manuscripts of the following texts:

   Note that the use of the term Apocrypha as a proper title is defined on this site as referring specifically (and exclusively) to the following listed texts (and the word should always be capitalized when used in this manner on this site). It is known that other works such as the Gnostic gospels are commonly referred to as "apocryphal" texts, but as per our site standards only the below-listed texts constitute the Apocrypha.

   Texts and Additions to Esther and Daniel that are included in Roman Catholic, Greek, and Slavonic Bibles

   • Tobit
   • Judith
   • Additions to the book of Esther in Greek manuscripts
   • Wisdom of Solomon
   • Ecclesiasticus (Wisdom of Jesus, Son of Sirach)
   • Baruch
   • The Letter/Epistle of Jeremiah (6th chapter of Baruch)
   • Additions to the book of Daniel in Greek manuscripts
     • The Prayer of Azariah and the Song of the Three Jews
     • Susanna
     • Bel and the Serpent/Dragon
   • Maccabees (I & II)

   Texts in the Greek and Slavonic Bibles but not in Roman Catholic Bibles

   • 1 Esdras (in Greek; 2 Esdras in Slavonic; 3 Esdras in Appendix to Vulgate)
   • Prayer of Manasseh (in Appendix to Vulgate; included in some manuscripts of 2 Chronicles / Paraleipomenon)
   • Psalm 151 (included in Greek manuscripts of Psalms)
   • 3 Maccabees

   Text in the Slavonic Bible and the Latin Vulgate Appendix

   • 2 Esdras (3 Esdras in Slavonic; 4 Esdras in Vulgate Appendix)

   Text in an Appendix to the Greek Bible

   • 4 Maccabees

   Care should be taken to clearly refer to relevant sections of the Apocrypha as text/book titles, chapter and verse sections as well as the order of content is not consistent between many translations, manuscripts, and critical texts.

   ---

   New Testament

   All extant manuscripts of the following texts:

   Homologoumena

   • Gospels
     • Matthew
     • Mark
     • Luke
     • John
   • Acts of the Apostles
   • Epistles/Letters
     • Romans
     • Corinthians (I & II, although historically they are believed to be the II & III letters sent to Corinth, the first of which is extinct)
     • Galatians
     • Ephesians
     • Philippians
     • Colossians
     • Thessalonians (I & II)
     • Timothy (I & II)
     • Titus
     • Philemon
     • I Peter
     • I John (not to be confused with the Gospel of John)

   Antilegomena

   • James
   • Jude / Judah
   • Hebrews
   • II Peter
   • John (II & III, not to be confused with the Gospel of John)
   • Apocalypse of John / Revelation

   These are the primary texts which constitute 'the Bible.'