As in the real life Navy, there are some differences between the role of Commodore and Fleet Captain in the Star Trek universe. There have been several Starfleet Commodores over the years, with the most notable being Commodore Geordi La Forge (LeVar Burton) in Star Trek: Picard season 3. The role of Fleet Captain is less represented across Star Trek history, with only two Starfleet officers known to have held the position: Fleet Captain Christopher Pike (Sean Kenney) and Fleet Captain Garth (Steve Inhat). A century later, Captain Carol Freeman (Dawnn Lewis) was offered the position of Fleet Captain of the ill-fated Texas-class line of starships.
While Fleet Captain is a promotion, it's unclear if it outranks Commodore, but both ranks sit underneath Vice Admiral in the Starfleet hierarchy. In Naval tradition, a Fleet Captain was essentially Chief of the Admiral's staff, which is why the title was retired in favor of Chief of Staff. It's known that Star Trek: Strange New Worlds' Captain Christopher Pike (Anson Mount) will eventually leave the USS Enterprise to take up the role of Fleet Captain. Here's what the role could entail for PIke, and how it differs from Geordi's role as Commodore.