There are two distinct Gospels. The Gospel of the Kingdom (circumcision) and the Gospel of Grace (uncircumcision).
Galatians 2:7-8
7. But contrariwise, when they saw the Gospel of the uncircumcision was committed unto me, as the Gospel of the circumcision was unto Peter
8. (For he that wrought effectually in Peter to the apostleship of the circumcision the was mighty to me toward the gentiles
But that passage, as has been pointed out before, doesn't talk of 2 different gospels, but two different people groups. Note that the second use of the word "gospel" is added by the translators for better readability. You can tell this is the case because of the use of italics in printed versions (probably in most online versions as well). Note also that it is still readable without the 2nd use:
Galatians 2:7 KJV — But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as
the gospel of the circumcision
was unto Peter;
Here's the same verse without the italicized/added words:
Galatians 2:7 KJV — But contrariwise, when they saw that the gospel of the uncircumcision was committed unto me, as of the circumcision unto Peter;
That makes it pretty clear, imo, that it was one gospel, two people groups. But in case you missed it there, Paul follows with a parenthetical (see your post, beginning of vs 8) to explain, that it was the apostleship of the two groups that was so divided, not the gospel:
Galatians 2:8 KJV — (For he that wrought effectually in Peter to the
apostleship of the circumcision, the same was mighty in me toward the Gentiles
But in case that wasn't yet clear enough, Paul reiterates in the following verse (which you didn't quote), which, once the parenthetical was closed, is the concluding point of verse 7.
Galatians 2:9 KJV — And when James, Cephas, and John, who seemed to be pillars, perceived the grace that was given unto me, they gave to me and Barnabas the right hands of fellowship; that
we should go unto the heathen, and they unto the circumcision.
"That we should go" is a phrase that comes from the idea of apostle, which means "the sent one".
To wrap up, Paul was the apostle to the gentiles (uncircumcision), and Peter and the rest were apostles to the Jews (circumcision)--with the same gospel, that Jesus died and rose again, defeating death.
