I rather like the idea that
@Christopher propounded in his (excellent) "Rise of the Federation" novels.
He suggested that the early Starfleet was composed of fleets provided by the founding member worlds, and that each of those fleets was responsible for a different area of specialization. He also suggests that the different uniform insignia we saw in TOS were intended not to be different SHIPS, but all of those different 'sub-fleets'.
As per
@Christopher's suggestion, here's a breakdown:
- Vulcan Space Central: Research and development. Example: USS
Intrepid ("The Immunity Syndrome"). Insignia: IDIC symbol. (We never actually see any of the
Intrepid's crew but I'm just guessing that's what they would have worn.)
- United Earth Space Probe Agency: Exploration. Example: USS
Enterprise. Insignia: Arrowhead.
- Tellar Space Administration: Logistics and supplies. Example: USS
Antares ("Charlie X"). Insignia: Hoof.
- Andorian Empire: Military defense. Example: USS
Constellation ("The Doomsday Machine"). Insignia: Pretzel.
- Alpha Centauri Space Research Council: R&D, probably the same as the Vulcans. Example: USS
Exeter ("The Omega Glory"). Insignia: Rectangle.