"Rap" only describes the singing style (e.g. no tonal singing just rhythmic chanting). "Hip hop" is a term for general music style, which includes rapping, scratching, beats, sampling, and the dance too.

As for sub-genres. In 'pure' hip-hop (later there was much mixing, see f.e. nu-metal), as I understand it, the main sub-genre distinction was East Coast vs. West Coast. Gangsta rap (which developed into the commercialised guns-fast cars-drugs-lewd women thing I find as attractive as ceebs does) was a variation that more or less pushed out other hip-hop within both.

I don't think we can speak of a "white" sub-genre in any sense, even in tone. I think we can speak of a minority of US white rappers, neither of whom fits easily into the previous two genres. Notably, Vanilla Ice, whom I'd call Mr. Wannabee; Beastie Boys (you know them for 'fight, for your right, to paaaaaarty'; I think 'Sabotage', below, is their best, also as video), who AFAIK are East Coast-inspired but built on punk and funk; and Eminem, who definitely grew out from 'black' hip hop, but in Detroit -- thus neither East Coast nor West Coast. (I see on Wikipedia that some now call it Midwest style.) That both Beastie Boys and Eminem sing in high nasal tones is accidental, less known white rappers and crossover style singers aren't like that. (Also, what about female rappers?)

_{*Lunatic*, n.
One whose delusions are out of fashion.}