My campaign is set in medieval Europe, so I'm dealing with slightly abstracted real-world denominations. Mostly the silver penny (or denier or denarius).
In my world (as in the real world) every kingdom, if not duchy and county, mints its own coin. Values are generally compatible, but coin in one realm is not generally spendable in another. In other words, if you have 300dn from Brabant, it's still worth 300dn when you travel to Aquitaine. But you'll have to get the coins changed or you may have trouble spending it.
This isn't completely accurate: In the real world, due to differing silver content, 300dn from Brabant might only fetch you 280dn in Aquitaine (or whatever). But that's more fiddly than I want to deal with. I like the story element of having to deal with currency compatibility; I don't like the maths and charts of having to deal with minor differences in value.
(An aside: The interesting thing about the medieval system is that, ignoring half-pennies and farthings (which are about as relevant to adventurers as D&D's copper pieces), the penny is really the only coin. The other denominations (shillings and pounds) are just amounts, not actual coins. (A pound is, literally, a pound. A pound of silver.)
(An exception to that: My players have recently had their first encounter with the new coin the Italian merchant states have started minting: the gold grosso, or groat. Worth 12 shillings, or over half a pound of silver. Never thought I'd see players eyes so wide over a bag of a couple hundred gold pieces!))
Bottom line: Yes, different coinage is relevant in my game, but only insofar as it serves the story. Where the coin comes from matters within the game world, but whether or not getting coins changes is an issue for the players depends on whether I want it to be.