Here we see a reference to two different gospels:
"But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as the gospel of the circumcision was unto Peter" (Gal.1:7).
If you look at he Greek transcript, the "good news" is only listed once like this:
I have been entrusted with the well message of the uncircumcision according as Peter of the circumcision.
Same gospel to two different audiences. Here's a better translation.
7 On the contrary, when they saw that I had been entrusted with the gospel to the uncircumcised, just as Peter had been entrusted with the gospel to the circumcised ESV
What was preached to the Jews during the Acts period? Here is what Paul preached to them:
"And straightway he preached Christ in the synagogues, that he is the Son of God...proving that this is the very Christ" (Acts 9:20,22).
Peter preached that Jesus was the Christ.
Acts 2:36
Let all the house of Israel therefore know for certain that God has made him both Lord and Christ, this Jesus whom you crucified."
In fact Peter and Paul preached basically the same message, which there is only one of, Christ. Acts 2 &13
Addressing Israel
Peter: 22 Ye men of Israel, hear these words;
Paul: 16 Then Paul stood up, and beckoning with his hand said, Men of Israel,
Christ descended from David
Peter: 30 Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne;
Paul: 23 Of this man's seed hath God according to his promise raised unto Israel a Savior, Jesus:
Christ died
Peter: 23 Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain:
Paul: 28 And though they found no cause of death in him, yet desired they Pilate that he should be slain.
David saw decay
Peter: 29 Men and brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulchre is with us unto this day.
Paul: 36 For David, after he had served his own generation by the will of God, fell on sleep, and was laid unto his fathers, and saw corruption:
Christ did not see decay
Peter: 31 He seeing this before spake of the resurrection of Christ, that his soul was not left in hell, neither his flesh did see corruption.
Paul: 37 But he, whom God raised again, saw no corruption.
Jesus resurrected
Peter: 32 This Jesus hath God raised up,
Paul: 30 But God raised him from the dead:
People witnessed the resurrection
Peter: 32 This Jesus hath God raised up, whereof we all are witnesses.
Paul: 31 And he was seen many days of them which came up with him from Galilee to Jerusalem, who are his witnesses unto the people.
Forgiveness of sins through Jesus
Peter: 38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
Paul: 38 Be it known unto you therefore, men and brethren, that through this man is preached unto you the forgiveness of sins:
Jesus is Israel’s savior
Peter: 36 Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.
Paul: 23 Of this man's seed hath God according to his promise raised unto Israel a Savior, Jesus: