Do they teach black and white people the same thing in beauty school? Does it depend on the school?

Yes, for the most part they do. There are probably schools that don't but the ones I know of have the same progress for all students of all backgrounds. Some people ume the opposite because for the most part you see whites at white salons and blacks at black salons, rarely a member from the opposite race is found in the shop with a high number of blacks or whites.