Onscreen, there isn't a difference. In the fourth season of ENT, we saw a logo that said STARFLEET COMMAND - UNITED EARTH SPACE PROBE AGENCY:
We also saw a UESPA logo by itself in the "Friendship One" probe in VGR and in the flashbacks in ENT: "First Flight." So maybe Starfleet was formed out of UESPA or merged with it. We know that the term UESPA continued to be in use throughout the 23rd century; Kirk mentioned it as the body he reported to in "Charlie X" and "Tomorrow is Yesterday," and its name appears on the Enterprise
-B's dedication plaque.
Perhaps UESPA continued to be used as a traditional name for the Earth Starfleet that grew out of it, or maybe Earth Starfleet was a subdivision of UESPA that eventually overtook the whole thing. And then when the Federation Starfleet was formed, the Earth branch of the combined service, which had formerly called itself Starfleet, went back to calling itself UESPA instead. Perhaps it and the Vulcan Space Command and the Andorian Guard and so forth continued to have some existence, at least in organizational terms, within Starfleet through the late 23rd century or so. But apparently the term had fallen out of use by the TNG era.