It differs in being retrograde, so to speak: the OT God is the God of Israel, but always, with hints, glimpses, promises, moving toward a day when all the nations would worship Him. From the earliest days, the Church understood itself as being meant for all men -- it was just a question of reaching them.
Islam is retrograde too -- in its own way, though it at least allows for conversion into the "tribe," even if it's enforced by the sword.
That's one way to look at it. But not the only way.
From the earliest days, the Church understood itself as being meant for all men
So is Judaism. The difference is that the Jews are the ordained clergy-nation, while the Gentiles are the Noachide congregation.
When St. Peter tells his audience "you are a priestly nation" who is he addressing, given that he was an apostle to the circumcision?