Well, it's hard to depict something with precision when you haven't the slightest idea of how it could work.
My understanding is that at one (or more?) point, the writers went to Roddenberry and asked how the Federation's economic system was supposed to work without money. Roddenberry admitted he was incapable of describing one.
The writers just wrote a Federation with money (purchases, banks, etc.) in some episodes/movies, while in other episodes/movies having someone state that money didn't exist.
Picard makes a purchase, then later states that money doesn't exist.
Jake earns money, then later says he doesn't need money.
In my opinion, there needs to be a way of combining the two positions, instead of embracing one and discounting the other.
Picard doesn't just live in a insulated Pollyanna bubble where he doesn't understand what going on around himself, he's accurate in his statements, although his statements perhaps don't necessarily tell the whole story.
It isn't a case of money only existing in the Federation only out in the "hinterlands."
Kirk can
truthfully agree with Gillian Taylor that "they don't use money in the twenty-third century," yet still buy and sell a house located on Earth, and Kirk did have the means of hiring a ship in TSFS (as did McCoy).
So what is the truth? Again I think it should
all be taken into account somehow.
Credits in the form of electronic financial transfers not being
considered "money" in the future, and the term money being reserved exclusively for money in a physical form in one possibility. A change in how certain words meanings have evolved.
This would line nicely up with Riker's statement that he doesn't carry money (for tip jars), money is something that is physical and carried. And maybe also Jake's situation where he (usually?) didn't need physical money, but did for a auction.
Thing with Jake's statement is that his seemed to be implying that the lack of need for money was a Human thing, and perhaps not beyond that species.
Picard as well, when speaking of money not existing, soon after directly mentions Humanity. Picard doesn't seem to be the type of person who would use the term Humanity generically to refer to all the species of the Federation.
So there, does the Federation as a whole also engage in money not existing? I could easily image individual members of the Federation retaining their own separate monitory system, while also making use of a interstellar form of money (the credit).