a.) A "human" biologically counts as an "animal".
b.) A "nonhuman animal" counts as an "animal" too, of course.

So what are the differences?

Maybe the factual definition of what a human being is, is more than "just taxonomie", and being a "human" is a kind of ideology or amounts to a state of ideology. And maybe being an animal is being given a bad name for being an individual nonhuman animal. Taxonomy does have a problem with individual nonhuman animals -- it doesn't count in factual individuals.