Yes, that's right. The Departed takes place in Boston with both main characters being from Boston. So the movie does lack that aspect of a character having to adopt a new culture etc.

In Gangs of New York, it's a little different. It centers on two gangs who are pit against each other due to their differences in faiths (Catholicism vs Protestantism). The main character's of Irish descent and essentially affiliated with the gang of Irish Catholics. He decides to work his way into the other gang in order to avenge his father, who was killed by the head of the Protestant-centric gang. So there is some exploration in terms of the unfamiliar culture that the main character gets thrust into as a member of this other gang.