Ok, my interpretation 
Note that DecTrek ranks Fleet Captain above Commodore and specifically equates it to Rear Admiral (one star), while the Star Trek Encyclopedia has them the other way around, and specifically categorises Fleet Captain as a Line rank, while Commodore is Flag.
On that basis, I think I'd go with the Encyclopedia, and swap the two in the PG.
With that out of the way, what do they represent, and what happened to them?
In TOS, we generally saw Commodores in charge of bases and some starships and the like, Fleet Captain just gets mentioned as a higher rank than Captain. Both are gone in the TNG era.
I reckon this has a lot to do with the way things have changed in the two time periods.
In the TOS era, Captains were often out of touch with SFC for a long time, and often had to make decisions with no input from superiors. However, it would occasionally be necessary to group ships together, and then you need a single commander. This is where the Commodore comes in - it's basically a rank for those Captains who nominally have command over two or more ships in an area (kind of a squadron commander), and have the power to make Federation-affecting decisions in their region. The Fleet Captain is the lowest rank of SFC itself, and specifically designates those staff officers having direct contact with the starship Captains. They are effectively the liaison with SFC. They may be based at SFC or in starbases, but as flag officers, they never have their own command responsibilies, they'd never command a starship or base for example.
By TNG's time, communications are much faster. The rank of Commodore is no longer necessary as Captains can liaise directly with their Fleet Captain, who is often based in a local system. When a squadron commander is needed, one Captain can be designated senior by the Rear Admiral, or the Admiral can take charge in person. The Fleet Captain rank is renamed Rear Admiral to make it clearer that this is a flag rank.
I'm also working on the common assumption that a line officer holds a physical command (vessel or base), a flag officer does not. When aboard another officer's command, a flag officer defers to the Captain in all operation issues, maintaining only a strategic point of view.
Does that make sense? I've tried to fit into Trek rather than the real world, so it may conflict with all those USN ranks 
Given that I'm working in the TOS movie period, this all becomes rather important, so please comment!
Jon
"There are worlds out there where the sky is burning, where the sea is asleep and the rivers dream; people made of smoke and cities made of song.
Somewhere there's danger, somewhere there's injustice, and somewhere else the tea is getting cold. Come on, Ace, we've got work to do."
THE DOCTOR, "Survival" (Doctor Who)