What is the difference between "called" and "chosen"?

Paul was chosen, his conversion was not his own free will. to this day, these types of conversions still happen.

Romans 8:30 explains those who are called.

the concept of predestination doesn't have much to do with your question.

I think the Church Fathers interpreted this verse as meaning that although we are invited by God, our actions will still determine our fate. Verse 14 needs, I think, to be considered along with the preceding verses:

Matthew 22:11–14 (KJV 1900)

And when the king came in to see the guests, he saw there a man which had not on a wedding garment: And he saith unto him, Friend, how camest thou in hither not having a wedding garment? And he was speechless. Then said the king to the servants, Bind him hand and foot, and take him away, and cast him into outer darkness; there shall be weeping and gnashing of teeth. For many are called, but few are chosen.

The Greek (Byzantine) commentator, Theophylact of Ohrid, explained the phrase Πολλοὶ γάρ εἰσιν κλητοί, ὀλίγοι δὲ ἐκλεκτοί:

"Many are called" for God calls many, indeed, all, "but few are chosen." For few are saved and found worthy to be chosen by God. For it is God's part to call, but to become one of the chosen or not, is our part. He shows, then, that this parable was spoken by the Jews who were called but were not chosen, as they did listen.

Explanation of The Gospel According to St. Matthew (Chrysostom Press, 1992).

Augustine seems to convey this same understanding, despite his being often cited as a source for doctrine on predestination:

And He saith unto him, Friend, how camest thou in hither not having a wedding garment? And he was speechless.” For He who questioned him was One, to whom he could give no feigned reply. The garment that was looked for is in the heart, not on the body; for had it been put on externally, it could not have been concealed even from the servants. Where that wedding garment must be put on, hear in the words, “Let thy priests be clothed with righteousness [Psalm 132:9]. Of that garment the Apostle speaks: “If so be that we shall be found clothed, and not naked” [2 Corinthians 5:3]. Therefore was he discovered by the Lord, who escaped the notice of the servants. Being questioned, he is speechless: he is bound, cast out, and condemned one by many.

I have said, Lord, that Thou teachest us that in this Thou dost give warning to all. Recollect then with me, my Brethren, the words which ye have heard, and ye will at once discover, at once determine, that that one was many. True it was one man whom the Lord questioned, to one He said, “Friend, how camest thou in hither?” It was one who was speechless, and of that same one was it said, “Bind him hand and foot, and cast him into outer darkness; there shall be weeping and gnashing of teeth.”

Why? “For many are called, but few chosen.” How can any one gainsay this manifestation of the truth? “Cast him,” He saith, “into outer darkness.” “Him,” that one man assuredly, of whom the Lord saith, “for many are called, but few chosen.” So then it is the few who are not cast out. He was it is true but one man “who had not the wedding garment. Cast him out.” But why is he cast out? “For many are called, but few chosen.” Leave alone the few, cast out the many.

It is true, that man was but one. Yet undoubtedly that one not only was many, but those many in numbers far surpassed the number of the good. For the good are many also; but in comparison of the bad, they are few. In the crop there is much wheat; compare it with the chaff, and the grains of corn are few. The same persons considered in themselves are many, in comparison with the bad are few.

How do we prove that in themselves they are many? “Many shall come from the East and from the West” Whither shall they come? To that feast, into which both good and bad enter. But speaking of another feast, He subjoined, “and shall sit down with Abraham, and Isaac, and Jacob in the kingdom of heaven [Matthew 8:11]. That is the feast to which the bad shall not approach. Be that feast which now is, received worthily, that we may attain to the other.

The same then are many, who are also few; in themselves many; in comparison with the bad few. Therefore what saith the Lord? He found one, and said, “Let the many be cast out, the few remain.” For to say, “many are called, but few chosen,” is nothing else than to show plainly who in this present feast are accounted to be such, as to be brought to that other feast, where no bad men shall come.

Sermons on the Lessons of the Gospels, Sermon XL

The general consensus from the commentaries I've seen on this, as well as the teachings of my Church, taking all of Matthew 22 in context is that the invitation for salvation is open to all, yet few actually choose to come to salvation.

How this fits in with irresistible grace, or pre-destination is not clear to me. Our denomination does not believe in irresistible grace. (We hold some Calvinist views, but not all). It's possible that the reason I'm only finding commentaries that support the idea of resistible grace is because my sources are biased, but the commentaries I've found seem to be united on this verse, with the possible exception of the Barnes' Notes on the Bible. (Second commentary quoted below).

Clarke's Commentary on the Bible (Emphasis mine)

Many are called, etc. - This verse is wanting in one of Colbert's MSS., marked 33 in Griesbach. See the note on Matthew 20:16. Many are called by the preaching of the Gospel into the outward communion of the Church of Christ; but few, comparatively, are chosen to dwell with God in glory, because they do not come to the master of the feast for a marriage garment - for that holiness without which none can see the Lord. This is an allusion to the Roman custom of raising their militia; all were mustered, but only those were chosen to serve, who were found proper. See the note on Matthew 20:16. Reader! examine thy soul, and make sure work for eternity!

Barnes' Notes on the Bible

Many are called, but few are chosen - Our Saviour often uses this expression. It was probably proverbial. The Jews had been called, but few of them had been chosen to life. The great mass of the nation was wicked, and they showed by their lives that they were not chosen to salvation. The Gentiles also were invited to be saved, Isaiah 45:22. Nation after nation has been called; but few, few have yet showed that they were real Christians, the elect of God. It is also true that many who are in the church may prove to be without the wedding garment, and show at last that they were not the chosen of God. This remark in the 14th verse is the inference from the "whole parable," and not of the part about the man without the wedding garment. It does not mean, therefore, that the great mass in the church are simply called and not chosen, or are hypocrites; but the great mass in "the human family," in the time of Christ, who had been "called," had rejected the mercy of God.

Matthew Henry's Concise Commentary

22:1-14 The provision made for perishing souls in the gospel, is represented by a royal feast made by a king, with eastern liberality, on the marriage of his son. Our merciful God has not only provided food, but a royal feast, for the perishing souls of his rebellious creatures. There is enough and to spare, of every thing that can add to our present comfort and everlasting happiness, in the salvation of his Son Jesus Christ. The guests first invited were the Jews. When the prophets of the Old Testament prevailed not, nor John the Baptist, nor Christ himself, who told them the kingdom of God was at hand, the apostles and ministers of the gospel were sent, after Christ's resurrection, to tell them it was come, and to persuade them to accept the offer. The reason why sinners come not to Christ and salvation by him, is, not because they cannot, but because they will not.

[snip]

The FourFold Gospel

For many are called, but few chosen. Many guests are invited, but few are accepted; because some neglect and despise the invitation, andothers cast dishonor upon the one who invites, by the self-willed andirreverent way in which they accept his invitation. In this parable thefirst parties invited represent the Jews; the city of murderers isJerusalem; the persons called from the highways are the Gentiles; theentrance of the king is the coming of the Lord to final judgment; andthe man without the wedding-garment is anyone who will be found in thechurch without a suitable character. The character of Christ is ourwedding-garment, and all the regenerated must wear it ( John 3:5 Ephesians 4:24 ; Galatians 3:27 ; Colossians 3:10 ; Revelation 19:8 Revelation 19:9 ).