: So it's natural (or should I say, impossible not) to
: confuse race with species, because the terms
: themselves are fuzzy and inherently confusing.
Not really. The only formal, scientific definition of species that I have heard is "two groups of organisms which can breed and viable offspring" (viable meaning that those offspring too can breed and have more of their kind, and so on, which is why horses and donkeys are separate species despite being able to make mules).
Different human races can all interbreed and have kids which can in turn breed with any other humans, so we are the same species. An even more extreme example is dogs - all the different species of dogs we know of, from Great Danes to poodles, are all classified as canis lupis, and barring extreme morphological problems (size differences, both in the reproductive organs and more importantly the size of the offspring compared to the mother) are all capable of interbreeding and producing viable offspring.