That makes sense. So UESPA is the branch of the government that oversees it and Starfleet is the organization itself?
Agreed, at least as far as Earth Starfleet. The idea doesn't seem to hold up though once the Federation comes into play. Why wouldn't Kirk say that he reported to the Federation and use the old Earth Starfleet's overseeing body? Unless UESPA was molded into the federation (which sounds logical, except why would it keep its pre-federation name?)