I've taken to calling treasure found in units of coins as well as generic currency as just “coins”. This allows an easy method for other DMs to put in whatever coinage they wish for the “standard” which fits their playstyle and group. Copper, Silver, or Gold standard works when you just call them coins.
But what about other types of coins?
 Porcelain. These coins are minted by a cosmic bureaucracy or an extremely omnipresent mining/trading company. Counterfeiters are targeted with extreme prejudice to avoid inflation of the coins. Every time you are struck by a mace or take a fall, multiply the damage x10 and you lose that many coins you are carrying from being smashed.
 Tea. These “coins” are a common term for those round tea-bricks, which are used as a common trading currency. Each “coin” can be put into a cup of boiling water to create a sort of coffeesque drug, and it is extremely common. Grants the user +1 to their first saving throw of the day. Grown in 700 mystic orchards in not!Tibet.
 Ivory. Coins are cut from a specific section of a specific animal's horn or tusks. The animals are quickly being hunted to extinction, naturally.
 Shells. “Coin” is just a common term used to describe a very common and universal type of shellfish shell, such as a cowrie or wampum. Used as a trading currency.
 Devil Coins. This setting's universal currency uses magic devil coins that automatically shift to look as valuable as possible to the person viewing them. The coins usually look shining, golden or platinum, with the faces of emperors or attractive women on them. Those with true sight usually just see a bored imp crudely sketched onto a piece of limestone.
 Graces. Each coin looks to be made of white marble, and may glow softly in a church. These coins represent a single good deed or pleasure one may experience in heaven; and can be traded amongst the living and the dead. Wealthy people want to be buried with as many of these as possible, so they have them at hand while they wait to have all their good deeds tallied up and given their salary.
 Magic. Coins are literally a compressed form of arcane or elemental energy; similar to Dust in Endless Legend or Endless Space. The reason enchanted items take so much money to make is not due to the cost of research or finding rare reagents, the magic coins are literally infused into the item or to call spirits and bind them within.
 Fuel. Coins are like slivers of supercoal, capable of burning hot and clean for a long time. Used among traders and crafters due to their inherent usefulness. Especially fitting in eternal winter style settings where everything is cold and shitty.
 Toys. They're just wooden chips, painted with designs and colors. Money is exclusively created and used by the fae-children of the forest. Even if you try to duplicate it, they just automatically know what is a legitimate piece and what isn't. Humans often trade with the fae-children for passage, blessings, or magic spells and have since adopted the currency. Among humans the currency has strict values, but among the fae-children it's a bartering currency which fluctuates on a whim.
 Artifacts. All the coins currently in use are ancient and made by the magical/technological precursor race. The method of creating them or replicating them is totally unknown, as is the metals that go into their unique orange and green hue. Adventurers digging up money from a tomb are literally getting first dibs on coinage; they don't even need to see a merchant to exchange it for cash.