I think it's a good question.
Star Trek's fetish for the word "Humans" has always seemed pretty weird. It's Terrans!
AFAIK, it all comes down to species versus place of origin. Our species is human, but our planet of origin is Earth/Terra. We can be referred to as human, by our country of origin, or by Terran--it all depends upon the context.
On a local level, you can be born of a certain country, and you'd be referred to within the confines of Earth as being from that country (e.g. American, French, Irish, etc), but that doesn't indicate your species, nor subdivision within (i.e. race). A person will be called Irish because they were born in Ireland, and the dominant race there is Caucasian. But you could easily be of another race and still be referred to as Irish.
I've no doubt that on Vulcan, there are a number of variations on the "homo sapien" beings. Is it just a coincidence that both the species and planet are both called Vulcan? I think so. When Spock talks of his physiology, he says he is Vulcan. He doesn't mention any other designation. Unlike someone from Earth, who would say they are human in physiology, not Terran.
So, it's up to the writers to pay attention to an appropriate level of being classification. Certainly with the Klingons, their homeworld isn't called Klingon or Klingonia. It's Qo'noS. In some cases, writers made that distinction while in others they didn't. I guess it all depends upon how much attention will be paid to them (guest versus recurring beings).