I'm pretty sure the patches shown all relate to the type of unit, ship or base the individual was assigned to, and rank plays no role. I have no idea why Commodore Wesley wears a Starfleet patch... all I can figure is that it was somehow intended to indicate he wasn't the Lexington's permanent captain.
I am unable to follow any of these theories that Commodore Wesley was temporarily in command of USS Lexington
for an excercise
(and at the expense of its John Doe captain).
- As we saw in "The Doomsday Machine" it's not unusual for a Commodore to have a starship command
- Wesley addresses Kirk on a first name basis (and vice versa). It's an expression of the familiarity among the elite starship captains, in contrast the tone between Kirk and other Commodores (bureaucrats) is strictly formal.
- Kirk and Spock make several comments about Wesley that suggest these references are made to Wesley as a starship commander: "Commodore Wesley is a dedicated commander. I should regret serving aboard the instrument of his death." (Spock) - "Any other commander would have simply followed orders and destroyed us, but I knew Bob Wesley." (Kirk)
Every seven years in the TOS and movie era (maybe a Vulcan touch) Starfleet upgrades uniforms, hardware and the Starfleet insignia changes (possibly to honor the accomplishments of Starfleet's best starship/s).
Pike's accomplishments may have lead to the adoption of the Enterprise's
delta insignia for Starfleet which we still see in "Court-Martial" at a time of transfer (Lexington's
flower is in the progress of replacing all delta insignias except for the individual insignias of starships like the Enterprise
And another hint is the unique size of Wesley's command chair (in contrast to those aboard Enterprise, Exeter
). That tells me: Starfleet's flagship (and Commodore Wesley is the kind of guy I'd be expecting to command the Federation's flagship).