Let's take a step back and go back to the three pillars of currency. The consensus is that for something to be a currency it needs to be:
* a store of value
* a medium of exchange
* a unit of account
You can stake another step back and say "what does value mean?" If a currency is "shells" then presumably it's that way because everyone values shells. If you don't value shells then the currency is worthless.
In short, value is what everyone agrees value is.
Now let's go back to when the gold standard was in effect. Back in those days you could exchange your USD for some amount of gold. Great! But so what? Today you can also exchange your USD for some amount of gold - it's just the amount is variable depending on market conditions instead of fixed.
So what's the difference between the two scenarios? Nothing, really. The "fiat currency" people try to argue that removing that fixed peg suddenly invalidates a currency. In reality the value of a currency is pretty much (and has always been) determined by how useful other people believe that currency to be. All of the "full faith and credit" etc are there to provide a foundation for that belief. For example, the US government has never defaulted on its debt obligations, including the pre-colonial debt obligations. That provides holders of the currency with a pillar on which they base their belief in the USD. In addition, the USD is used in trillions of dollars per day of transactions, bolstering its mindshare.
Digital currency is sort of the ultimate evolution of that idea of value being belief based, because there's literally nothing behind digital currency except belief...period. There is no "full faith and credit." Nobody stands behind it. That's why it's amusing that digital currency fans try to denigrate real currency by calling it "fiat currency." Digital currency is the ultimate fiat currency, in that its value is completely based on belief.
As an aside, hyperinflation occurs when people basically lose faith in the value of their currency, so the government tries to print more currency...which reduces the perceived value...which causes people to lose faith...etc. It becomes a death spiral.
The US is unusual because it seems to be able to print as much money as it needs without ill effects. If other countries behaved as the US does they would have the IMF at the door and debt markets abandoning it.