I originally wanted to use the term 'race', but ironically I decided it was too controversial. There's no single term to adequately describe all these groups.

Although swirling pupils are not normal to humans, I guess you have a point about the Al Bhed being a race. Still, humans can interbreed with Guado in addition to Al Bhed, and Guado are definately not human. It's kind of like lions and tigers interbreeding, possible but unlikely in nature.