In TNG, Picard says that the Federation has evolved past a need for money. Indeed, we never see any.
In DS9 though, Quark talks a lot about bar tabs and costs. Surely O’Brien and Bashir don’t get free drinks, so how do they pay? I’d assume that any Ferengi worth his lobes won’t accept anything that can be replicated, so do Federation officers get a stipend of tradeable “value” when interacting with cultures that still expect payment?
I think there’s also a reference to Quark paying rent to Sisko for running the bar. Presumably that’s denominated in latinum. I wonder where it goes? Maybe the secret “Garak black ops” fund.
I always assumed the rent went to the Bajorans. After all, it’s their station, Sisko just runs it for them.
As for the bar tabs, I don’t think they ever really explained how starfleet officers paid for stuff on DS9. I always just assumed they had some kind of credit account through Starfleet or something when they were posted there.