The short answer is that it is far from a settled question - many people say “Homo sapiens neanderthalis” as the proposed subspecies. The fact that modern humans and Neanderthals crossbred and apparently had viable offspring is strong evidence for this understanding (but not necessarily conclusive; sometimes mules are fertile).

That said, Neanderthals rapidly went extinct after modern human contact, and are vastly genetically different from us compared to any two randomly chosen modern humans. They do not appear to have formed especially sophisticated technology or formed any society as complex as a simple tribe. So there are still meaningful biological differences between Neanderthals and modern humans that don’t require the delicate machinery of anthropology to understand.

Note: a difficulty here is that “species” is actually a very fuzzy concept, one that Nature itself doesn’t seem to care much about. “Subspecies” is even more vague.

Outside of modern humans (Homo sapiens sapiens) there had been only one other conclusively identified “race”[1] of Homo sapiens, the Homo sapiens idaltu. Perhaps there will be more evidence to put Neanderthals in there as well, but the consensus is that they were a separate but closely-related species.

[1] “Race” in the scientific sense as a synonym for subspecies, not the social sense of “ethnic group, but with more negative overtones.”