"Gospel that Paul preached as the apostle to the Gentiles in Galatians"

In the letter to the Galatians, Paul is calling himself an "apostle to
the Gentiles(2:8)" comparing himself to Peter who was an "apostle to the
Jews". So does that mean that they were preaching two different Gospels?

- 1:6-2:14 The Truth of the Gospel

As Paul is calling himself an "apostle to the Gentiles(2:8)", he was
called to preach the gospel especially to the Gentiles. So in Paul's day
the gospel was prevalent among big number of people. But at the same
time, some Jews forced the Gentiles to be circumcised and also to keep
the law of Moses. Because they believed that the circumcision is
required for the salvation. So this problem between Jews and Gentiles is
one of the key theme in this letter.

- 2:15-4:11 Justification and the Fulfillment of the Law

Jews believed that salvation will only be given by keeping the mosaic
law and performing circumcision. But this ceremonial law was fulfilled
by Jesus Christ so salvation was given to all the people who believe in
Christ. Not like in the old days when salvation was given to those who
kept the old covenant.

So what was the purpose of the Law? One of the purposes was to reveal
people's sins to themselves till the day of the Christ's sacrifice on
the cross. So the law is not something that goes against the promise
that was given to Abraham and the seed. The Abrahamic covenant's promise
is that the people will be saved through faith in Jesus Christ and not
by the works of the law. And that is the justification that Paul is
speaking of in this letter.

- 4:12-5:6 Brothers of Christ

The people who believe in God will be Heavenly Father's children. And
they will also be His heir that inherit the kingdom of God with His Son
Jesus Christ. And this is the fulfillment of the promise and the
salvation. Paul is calling the people who is under the Abrahamic
covenant "the son of free woman" in the comparison to "the son of slave
woman" who is under the Mosaic law. The son also means the heir so the
people who will be saved through faith in Christ will inherit the
kingdom of God. Because we are the brothers of Christ. And this is the
justification.

- 5:7-6:16 The Great Commandment

Salvation will be given through the faith in Christ and not through the
ceremonial law. But it does not mean that the law was meaningless or
bad. Or it does not mean that there is no connection between the faith
in Christ and the Mosaic law. But the Mosaic law was summarized　into
two commandments as Jesus taught the Pharisees　in Matthew 22:37-39,
"love the Lord your God with all your heart and with all your soul and
with all your mind." and "love your neighbor as yourself.". And this is
the fulfillment of the Mosaic law that was done by Jesus Christ.

So by loving our brothers and sisters in Christ, we still keep the law
but not the Mosaic law it self. But the Mosaic law that was fulfilled by
Christ. Because Jesus Christ didn't come to abolish the Law(Matthew
5:17) but to fulfill the law. And so keeping those two commandments of
love which is also called "the great " is the way we should live and
walk in the Spirit(5:25).