There's probably four or five *major Boston accents with subdivisions of each one. You have some that are primarily regional and some that are ethnic, but the difference between regional and ethnic can be hard to pin down since the different ethnic groups tend to clump together in different regions. It's been years since I've lived there but I would think that Cliff's accent was sort of a Southie accent.

Then there was the time I was at a play that had a character who was supposed to be southern. the actor's accent was an OK generic "southern for the yankee audience" accent but it kept slipping up to a Down East accent in the middle of a sentence. Rather disconcerting, really.