I think that the Federation Starfleet as an outgrowth and expansion of the Earth Starfleet. Not the same organization exactly, but not a completely different one as well.
Obviously, I think we are meant to believe that this organization, and the UNESPA, *became* the foundation of the Federation Starfleet. All those ships and that infrastructure and the Academy and personal weren't just forgotten about and trashed, they transitioned to become the Fed Starfleet. Just like the Bajoran Milita was supposed to be in DS9.
There are tow many similarities. (The uniform color scheme, for example.) And they didn't just discard all those personal and ships and starbases infrastructure, they used it as a foundation.
Hell, even in Kirk's time, and as late as Picard's, there was talk that other Federation species had their own separate fleets. We had almost all Vulcan and all Human ships, etc...and in Picard's time, we still had all Vulcan ships, and an exchange program with the Benzites.
Starfleet *should* have been the Federation navy/defense/exploration arm...but often it was *treated* as a Human organization. They never really were exactly clear on that. In TU, we saw ALL human admirals running the fleet at the HQ on Earth. Where the Vulcan and other Federation memeber species.
At times, it was like Starfleet was just the Earth space navy, and at others like the Federation navy. Spock, it was *implied* was the first Vulcan in Starfleet. Until T'Pol, people took it for granted that he was.
Now, Enterprise was the first Starfleet warp 5 ship (and if *I* had created Enterprise, it would have been the first starship ship) period. But yeah, we had those older arrowhead and Intrepid style warp 3 ships. And Travis made mention of seeing pictures of previous Starfleet captians when he went to that Academy, or wherever he underwent Starfleet training. (It was when they were Trying to take a pic of Archer to hang there as well.)
But it was weird because in that episode about teh tests of the NX-Alpha and NX-Beta, they were just trying to break Warp *2*. I assume that was warp two with the new style of Warp 5 engines, but it almost seemed like Starfleet itself was trying to build the first engine that went Warp 2. But other times, they implied there had been a Starfleet previous to Enterprise for several decades.
Just like the thing about whether Starfleet was a Human/Earth or a federation organization, they really didn't seem to have thought too deeply about Starfleet history.
Honestly, Enterprise should have been a show about the FIRST Earth Starfleet, IMHO.