What different standards for currency can we be on?

Ghana’s cedi is named after the seashells they used to use as currency.

After the nuclear holocaust next year, bullets.
Or bottlecaps, if you are into fallout nonsense.

^ Bullets, booze, and can openers.

Barter

Currency can be pegged to any commodity, or to other currencies. Or commodities themselves can be used as currency. Cigarettes were popular in post-WWII Europe.

There are also private currencies that might be accepted within certain groups.

The full faith and credit of the United States. There is no reason to base a currency on anything other than as an agreed store of value.

Economics will cause an economy to arrive at an agreed value. Price something to low, and it will be bought up; price it too high and no one will buy. Equilibrium will be found.