No, Paul had only one Gospel. And if he said Peter and James were in agreement with him, then they all had the same Gospel, in the eyes of Paul. Peter most certainly did *not* acknowledge that Paul was preaching a different Gospel!
Gal 1.6 I am astonished that you are so quickly deserting the one who called you to live in the grace of Christ and are turning to a different gospel— 7 which is really no gospel at all. Evidently some people are throwing you into confusion and are trying to pervert the gospel of Christ. 8 But even if we or an angel from heaven should preach a gospel other than the one we preached to you, let them be under God’s curse! 9 As we have already said, so now I say again: If anybody is preaching to you a gospel other than what you accepted, let them be under God’s curse!
When James and Peter acknolwedged that Paul had the same Gospel, even though he was preaching among the Gentiles, it was an assertion that they preached the exact same Gospel. Cultural trappings aside, there was no effort by James, nor by Peter, to affirm the continuing legitimacy of the Law of Moses. Paul, James, and Peter all believed that Jesus had completely fulfilled the Law. James called it the "Law of Liberty."
Gal 2.6 As for those who were held in high esteem—whatever they were makes no difference to me; God does not show favoritism—they added nothing to my message. 7 On the contrary, they recognized that I had been entrusted with the task of preaching the gospel to the uncircumcised, just as Peter had been to the circumcised.