the paper bank note being an alleged proxy for something real
As soon as people started offering notes as proxies their value depended on belief that there was something real to back them. That might have been true but not necessarily so. It helps if there is some form of regulation but there is a limited capacity for regulators to make good any defaults which is why we've seen complex
conjuring tricks financial management for the last decade or so.
Coinage is also a form of regulation. By providing allegedly fixed amounts it sets out to ensure that you have the amount of precious metal you thought you had without having to weigh it out at every transaction. It's no coincidence that coins bore a symbol of the state where they were issued because the state was the regulator. Of course because the state had a vested interest in the coins being circulated there was always a temptation to try to profit in the short-term by taking advantage of its regulatory function to debase the coinage. There was also the temptation for private enterprise to help itself by coin clipping but the state had ways of dealing with competition like that.