But Barnabas took him, and brought him to the apostles, and declared unto them how he had seen the Lord in the way, and that he had spoken to him, and how at Damascus he had preached boldly in the name of Jesus. (ASV)
Acts has Paul meet all of the disciples in Jerusalem shortly after his conversion. Paul himself says in Galatians that his first visit to Jerusalem occurred three years later. When he did finally go up to Jerusalem, he says he visited only Cephas and James (the Just). He makes a very firm declaration that this is not a lie! (Gal 1:18-20)
In Acts 9, we are told:
26 And when Saul had come to Jerusalem, he tried to join the disciples; but they were all afraid of him, and did not believe that he was a disciple. 27 But Barnabas took him and brought him to the apostles. And he declared to them how he had seen the Lord on the road, and that He had spoken to him, and how he had preached boldly at Damascus in the name of Jesus. 28 So he was with them at Jerusalem, coming in and going out.
This compares with the account in Galatians where Paul tells us:
1 Then after fourteen years I went up again to Jerusalem with Barnabas, and also took Titus with me. 2 And I went up by revelation, and communicated to them that gospel which I preach among the Gentiles, but privately to those who were of reputation, lest by any means I might run, or had run, in vain.
We have the earlier reference to visiting Peter:
18 Then after three years I went up to Jerusalem to see Peter, and remained with him fifteen days. 19 But I saw none of the other apostles except James, the Lordâ€™s brother.
We have two separate events described. The visit by Paul to Peter would have occurred earlier than the visit that required the intervention of Barnabas to get the apostles to accept Paul.
Edit this section to note miscellaneous facts.