Buddhism isn't concerned with genetics, the phyla of biology, or social categories like race. When Buddhism talks about 'realms of reincarnation,' it is referring to the incarnation of certain mental structures or fixations. In the human realm one is capable of pursuing liberation consciously; in the animal realm conscious activity is overshadowed by more primal instincts, cravings and urges; in the ghost realms one is trapped entirely in karmic patterns... Some groups interpret that as reincarnation into an actual human, animal, or ghost-like being, other groups take it more as metaphor, other groups don't subscribe to the 'realms' tenet at all. Buddhism is diverse.
'Realm' is used to suggest self-enclosed worldviews, the way we might oppose the 'realm' of physics against the 'realm' of poetics. Don't read more into it than that.
I do feel the need to point out that the concept 'race' is not ontological. It is a thoughtless, reactive categorization system that wells up (as certain Buddhists might say) from the karma of the ghost/animal realms. Those who take race as a serious concept are trapped in a karmic pattern; they won't reach liberation until they shake it off.