Money is seen as having four principle functions:[1]

1. A medium of exchange.

2. A unit of account.

3. A store of value.

4. Sometimes, a standard of deferred payment.

Function 1 is currency. Function 2 is value. Function 3 is as an asset. Function 4 is debt.

Note that debt also needs to have some sense of value, and that effective debt-management systems tend to rely on a stable metric of value.

William Stanley Jevons writing in Money and the Mechanism of Exchange (1875)[2] gives seven qualities of the material of money: utility/value, portability, indestructibility, homogeneity, divisibility, stability, and cognizability.

By utility, he holds that money must have an intrinsic value of itself. Given the existence of nominal coinage and fiat currencies, this is clearly false.

By portability, that money is easily transported and exchanged, unlike other assets, say, land.

By homogeneity, that any given unit of money is equally exchangeable for another. It doesn't matter what dollar, euro, yen, or mark you have, only how many.

By indestructibility, somewhat relaxed, that money not be easily or spontaneously degraded. Volatile or uncontainable forms of assets are not suitable for money.

By divisibility, that the units of money be either subject to division or multiplication. Unlike, say, a Great Masters artwork, which has value, is portable, and is reasonably durable, but whose value does not survive its being cut into pieces. Contrast a dollar which can be subdivided into pennies, or aggregated to a $100 banknote.

By stability, that the value is reasonably uniform over time. As with utility, this seems not strictly true.

By cognizability, that money is immediately and universally recognisable as money. Note that this argues against certain suggested money alternatives, such as bitcoin, which literally requires a planet-wide network of extraordinarily expensive computations to be computed to "cognize" any given transaction.

The history of debt and money shows numerous forms, including "gift cultures" (generally for small tribes), grain accounts (early cities), numerous commodities (metals, stones, beads, glass, beaver pelts, oyster shells, cattle, cattle hides, and more. (Many of these origins show up in slang terms for money.) Virtually all currencies have or had names suggesting either weight, divisibility, quality, domain of relevance (typically country), or some indicator of quality, of coinage: pound, shekel, dinar, dollar, mark, royal, florin, ruble, afghani, and many more.[3]

Examples of currencies not representing government-issued coin (or other demarcations) are commonplace, and range from other governments' currency (as in US dollar trade or black markets outside the US, or use of Spanish Reals in colonial America and the early US) to former governments' currency (Roman coinage being used long after the fall of the Roman Empire), to commodity currencies based on raw materials (such as beaver pelts and oyster shells) to manufactured products such as cigarettes. A classic example of the last is given in "The Economic Organisation of a P.O.W. Camp", by Richard Radford, describing the cigarette-based economy of a German WWII camp.

My own view is that money (or debt) is information, specifically socially recognised recognition of obligations, and in its manifestations, tokenised money represents some credible expression of that obligation. In form, then, money is whatever commodity forms the most universally acceptable and available medium of exchange within a given exchange network. This might be a government-issued coinage, but can be something else. The classic functions and Jevons' list of qualities are not absolutes, and there can be considerable trade-offs amongst these.

An element explicitly mentioned in either the four functions or Jevons lists is trust evidenced in money. In tightly-knit tribal structures, the trust is manifest and tokenisation is not required. Credits and debits are known, disputes are readily settled, and explicit tokenisation is not required, so money does not exist. In early cities, grain and other commodities served as both principle exchanged goods, and principle units of value, and an accounting system with an annual cycle functioned relatively well. As trade and exchange expanded in both goods, distance, and numbers of participants, an explicit tokenisation was required, and uniform assets with concentrated stable value and assayable quality (mostly precious metals) emerged. The notion of seigniorage, a premium paid for coinage based on its minting, above the specie metal contained within it, is a measure of trust in the mint. Paper, fiat, and non-work-factor digital currencies have effectively infinite seigniorage -- there is no intrinsic value, instead the value is in the trust of institutions and systems of account.

NB: This may be a minority view of one.

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Notes:

1. https://en.wikipedia.org/wiki/Money#functions

2. https://archive.org/stream/moneyexchange00jevorich#page/n7/m...

3. For a list of currencies, see https://en.wikipedia.org/wiki/List_of_currencies Etymologies may be traced via the online etymological dictionary, https://www.etymonline.com/

4. See https://news.nationalpost.com/full-comment/frances-woolley-t... Original paper: http://www.simon-davies.org.uk/Radford_1945_POWCamp.pdf