Technically "species" is also incorrect, since many D&D races can produce fertile offspring, whether half-breeds or otherwise (half-elf and half-orc have been core races for ages)
You're describing the 'mate-recognition' definition of species, which does not rule out cross breeding because memebers of each species could be geographically isolated but still compatible.
Species, like race and all other human created categorical systems have edge cases, exceptions and oddities and mostly importantly different definitions!
There are many examples where species definitions get thrown out because biology does crazy things. From the all female salamander species which interviewed with other species, to the multi organism man-of-war jelly thing floating in the ocean, biology does crazy stuff that will forever confuse us humans.
Nowadays, in my line of work I now think of nucleotide distance between individuals... But even that metric is troublesome.
Sure, but it seems pretty much all D&D “species” can interbreed, in which case those are no longer edge cases and perhaps the word “race” makes more sense.
In D&D is there a history of how the different races came to be? Did they have some sort of diverging point from a single ancestor?