That is, traditional specie coin currency is standardised for quantity and quality, or at least is initially. Most states have found a need to devalue specie coin, and virtually any state with a sufficiently advanced financial system and institutional trust either settles on a fiat currency or adopts another country's fiat currency as its own standard. kragen is making a similar point here: <https://news.ycombinator.com/item?id=41895405>.
For the latter, see the U.S. dollar which is either the or an officially accepted currency: Turks and Caicos and British Virgin Islands (both British overseas territories); Bonaire, Sint Eustatius, and Saba (all Dutch municipalities); the independent states of Ecuador, El Salvador, Timor-Leste, Federated States of Micronesia, Republic of Palau, and the Marshall Islands; and quasi-official or widespread use in the Bahamas, Barbados, Belize, Costa Rica, Panama, Bermuda, Myanmar, Cambodia, Cayman Islands, Honduras, Nicaragua, Somalia, and Zimbabwe.
I've developed the view that seignorage, that is, the exchange value in excess of specie value of coinage, is effectively a measure of trust in a currency system, and that fiat currency in paper or even more so as ledger entries (written or electronic) express an extraordinary level of trust in a currency, the more so if that currency is widely accepted internationally.
Another interpretation is that money in a given economic region is the most widely accepted commodity, that is to say, the exchange medium which is accepted preferentially to any other. This need not be a conventional currency (e.g., commodity or symbolic exchange of shells, hides, cattle, cigarettes, alcohol, laundry detergent, etc.), or the official currency of a region (though legal sanction and sanction of discharge of debt go a long way to establishing a currency within a given region). Multiple currencies may trade simultaneously, possibly in slightly differing contexts, and through much of history there has been at least some distinction between retail trade (often copper), wholesale (silver), and capital / government financing (gold). Adam Smith discusses this at great length in Wealth of Nations. Multi-metallic systems often involve variable exchange rates between different classes of money, and I've mused that this might be something worth reintroducing to modern financial systems.