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How is currency value grounded?

I've been reading Proof of Stake lately. It's a collection of essays about cryptocurrency, cryptoeconomics, etc. by one of the creators of Ethereum, Vitalik Buterin. In one of the early essays Vitalik defines the seigniorage of a currency as the difference between the "face value" and the exchange value.

What I don't quite understand is how these terms "ground out." What defines "face value"? How is it different from "exchange value"?

I'm trying to understand at least the "toy economic model" story behind this. Say you have a gold coin labeled "25 schmeckels." Is that the face value? Just whatever abstract unit is written on it? Conceptually how could you even subtract "25 schmeckels" (whatever that is) from (the value of this gold coin)? It seems like a dimensional analysis error. It's not obvious that these two things, standing alone, are interconvertible. You need some kind of exchange. But how does that exchange work and why? I'm still trying to figure that out.