As Enterprise puts it, Starfleet was once shorthand for the United Earth Space Probe Agency Starfleet (of Star Fleet)...
Star Trek has always been a bit unclear as to whether (even in post-Federation/post-Enterprise times) Starfleet is a Federation "navy" or an Earth navy.
No, it really hasn't. The only times Starfleet has ever been referred to as an Earth "navy" were in early TOS, before they created Starfleet for "Court-Martial" and the Federation for "A Taste of Armageddon." Since then, Starfleet has been explicitly stated on multiple occasions to be a Federation
agency, answerable to the Federation
I am at the library, so I typed that in a hurry, and just went back and edited it a bit. But I've gotten the impression sometimes that Starfleet was an Earth-centric agency.
I do think that it IS the Federsation navy...but I gte the impression that there are all-Vulcan ships (Intrepid in TOS, and the ship in "Take Me Out To the Holosuite") and all Benzite ships (in that TNG exchange program episode)...so I wonder if, in some cases, individual species/worlds have that own Starfleet branch...so in TOS the Enterprise was a Federation Starfleet vessel, but operated by the UNESPA/United Earth Starfleet (branch.)
In STID, we saw several non-Human admirals in that briefing room scene, actually. And of course, we never know:
In Star Trek 6 and Into Darkness, we saw a roomful of Starfleet admirals - and they were all human.
1. How many of those Human-looking people actually are Human, or how many of them are non-Humans whose species looks Human. Or:
2. How many of those Humans are actually from Earth as compared to, say, former Earth colonies have have become their own separate, independent Federation Members, or to other planets that host large Human populations. For all we know, three or four Human extras in any given scene may be from Andor or Tellar.
Meanwhile, a preponderance of one species at one location does not make that organization an agency of that species's homeworld's government. If Starfleet's Tellar headquarters and Tellar-based fleet is mostly staffed by Tellarites, that doesn't mean Starfleet is a Tellarite agency.
Yeah, good points. I think there may be species-specific branches of Starfleet (which males sense if some species have different environmental and atmosphere needs)...as well as multi-species ships like the Titan in the books. (Plus in Voyager they said that Earth wasn't just a human planet anymore, but home to many species...and so individuals of those species would join the *Earth* branch of Starfleet.
And I really think that there would have to be at least a few Starfleet Academy branches out there too, since I don't see how one academy (which seemed to have a limited number of slots per Federation sector) - could staff all the ships and starbases that we saw in TNG and DS9. (But then again, in TNG and DS9 we were given different impressions of the size of Starfleet. They lost 40 ships at Wolf 359, and they acted like it was a significant fraction of the whole Starfleet...but then in the Dominio War arc in DS9 we saw whole fleets of ships, 40 or more even, go into battle, and most get lost. I think in one DS9 episode they mentioned losing 300 ships in a short amount of time! And yet Starfleet goes on strong.