Certainly can't speak for the Japanese, but as a former American, now Canadian, married to a Brit, I might suggest that Americans call themselves Americans, Canadians call themselves Canadians and sometimes get upset when Americans claim the whole hemisphere by that term, but don't have another suggestion (Yankee is a pejorative, usually). And British call themselves British, or English if their playing football.
These, by the way, are NOT races. These are nationalities.
A much more interesting question is what do the races call themselves - and how they can "get away with" calling themselves terms that those of other races are best to avoid!
Student or Learner