I mean, have you EVER referred to yourself as a 'Terran' or heard anyone else doing that???
I think the distinction between "Humans" and "Terrans" is quite meaningful once you have two or more human space nations *or* you have a nation that includes other species in addition to humans. After all, we currently refer to people as "Americans", "Chinese", "Russians" etc. and it's a meaningful real distinction to us.
Only the hippier types prefer and use "Human" exclusively over the political/national/ethnic labels...
So, the "Terran Empire", "Solarian League" or what have you is thus just a space nation centered on the planet Earth or the star Sol. If that is identical to a "Human Empire" that's just because you happen to have a special case where a) there are no other human space nations and b ) the humans form the majority or are the ruling species of the nation. Both could be otherwise.
Consider the setup of Honorverse. You have a "Solarian League" and a "Manticorean Empire". Both are human but still quite capable of going to war with each other, and the term "Human Empire" would be essentially meaningless or at best an Utopian concept in that universe.
Or, take the Trekverse: In the OS you had a "Federation" and a "Klingon Empire". The former was specifically not synonymous to "Human Empire" because it was a multi-species entity that while including the humans did not have them as the explicit rulers. Compare it to the Klingons who had conquered other species and thus also had a multi-species political setup, but their nation was still specifically the Klingon Empire implying that there were no other Klingon nations and that the Klingons were, indeed, the ones on top.