In my opinion, Starfleet in the 2260's consisted of numerous sub-fleets, each having its own insignia. So Enterprise
and the jerks in the officer's club in "Court Martial" are all in, say, the 1st Fleet (or maybe the EUSPA Fleet?) and Exeter, Constellation,
as per "In a Mirror Darkly") each belonged to different sub-fleets under the larger umbrella of Starfleet.