Isn't it possible there are ways of telling stories about all that sort of thing without necessarily requiring that the main characters must without exception be the crew of a starship on a mission of exploration?
It's called Star Trek
It would me like me turning on Marvel's Agents of S.H.I.E.L.D
and finding out that its a sitcom about an elderly islamic woman and how she copes with her grandson's Jewish wife.
And all that time on all the different shows when they weren't on a spaceship and weren't trying to explore anything at all, I suppose none of that was Star Trek at all?
If it's the name that's bothering you - I'm not sure how a show following various different types of ships can even be construed as not constituting a 'trek through the stars'.