Well, the Enterprise
had a mostly Earth-human crew, so maybe Starfleet was divided into different fleets under different planetary governments' administrations. The Starfleet we saw in TOS seemed very Earth-centric; maybe there were other subfleets that were Vulcan, Andorian, Tellarite, etc. The Intrepid
could've been under the supervision of the Vulcan branch of Starfleet, for instance.