...Why do you think the apostles were sent to the Jews, and Paul to the Gentiles? If it was the same Gospel, then it wouldn't matter who they went to. Why were the apostles told to stay in Israel and continue preaching to the Jews?...
First, this was a temporary situation, history shows that besides the Apostle James who was executed in early Acts, all the others died somewhere far away from Judea, so they all did fulfill the Lord's Great Commission, eventually.
And second in answer to your question it's a matter of 'liturgy' for the lack of a less 'Catholic' sounding word.
'Practicing' Jewish people ('Jewish' in an inclusive sense, including any converted Gentiles) celebrated the Old Testament, Levitical, Temple liturgy (which included whatever the dispersion did in their synagogues for local liturgy).
When these folks believed in Christ, they began celebrating the New Testament liturgy, which was 'Mass', again, for the lack of a less 'Catholic' or Orthodox sounding word.
So the Gentiles were familiar with their own liturgies of course, which included offering sacrifices on altars to pagan idols. Both groups were coming from a different liturgical tradition, and so when Paul was dealing with the primarily formerly pagan Gentiles, he expressed himself differently from how the other Apostles expressed themselves when dealing with the circumcision, who came from the Jewish traditional liturgy. But they were both preaching the New Covenant Gospel, the Gospel of grace as you put it. Paul calls it the 'New Testament' in 1st Corinthians.
Both groups of Christians, with different backgrounds, practiced the one and same New Covenant liturgy of the Church, though the pagans were told to avoid idolatry by Paul a lot more than the other Apostles warned the Jewish converts to the Church did, since their Temple liturgy was actually ordained by God, although it had obsolesced at Christ's sacrificial death, burial and Resurrection, and Ascension. And the other NT letters directed at those coming out of the Jewish liturgical tradition(s) spent more time reminding those people of scriptures from the OT, which foretold of the NC, and which corroborate it.
fwiw, and peace.
