Yes, but the difference also has to do with geography/preference. Brown and Polar bears can and do produce viable offspring, but because they're generally geographically separated we consider them separate species. Same for birds; many could mate but they choose not to (different mating calls, etc), and for that reason combined with different looks we classify them as separate species. Neanderthal, who are accepted as being a different species of human, interbred with humans before going extinct.

It's my opinion that if aliens visited earth 30k years ago and used our definition of the word, they would classify us as different species. To be clear I'm not advocating that we should refer to humans as different species, just that because we're capable of such advanced thought we should abide by different rules than we hold other animals to.

The definitional limit on interbreeding includes geography and preference; black/brown/polar bears can and do interbreed in captivity but because they live in different locations and they look sufficiently different/have different diets we consider them different species.

If Aliens landed on our earth 20k years ago and used our definition of the word there's no doubt in my mind they'd consider us different species, we'd be like bears. As far as I can tell the only reason we don't classify people as different species is for the sake of society, as people would naturally then try to determine differences and rank them, which has an obviously bad long-term outcome.