Fiat money does not have use value. It has utility as a money only to the extent that people are willing to trade for it. These people may and often do include an issuing state, though this is not a distinguishing characteristic. The name derives from the fact that it is "declared by fiat" to be money. However such a declaration is also not a distinguishing characteristic. Fiat is simply money without use value. Money with use value is referred to as commodity money.
While value is subjective, making it impossible to determine use value in practice, the classification itself is clear. Paper money can be burned for heat, but this is typically not considered a material use value. Bitcoin can be used for timestamping, but this is also not typically considered a material use value. Gold, silver, copper and other coinage is generally considered to have material use value. When a commodity money's face value becomes less than its commodity value, it has transitioned to a commodity and is melted or hoarded.
A money substitute is a contractual claim to a definite amount of money, redeemable on demand. As such a money substitute represents a "future good" while money is a "present good". Fiat is not a money substitute because it is not redeemable for any definite amount of money, it is the money itself. Debt is often securitized and guaranteed by the lender as a money substitute, known as a banknote. Given that value is subjective, it is also not possible to distinguish whether a person values the redemption, or the claim itself, but the assumption is generally that the redemption is valued, not the document it is written on. When a money substitute is abrogated yet still trades it has transitioned to fiat.
Representative money is often misinterpreted as a present good, yet because it is a claim (to what it represents), it is a money substitute. The gold-backed U.S. Dollar was a money substitute and the modern U.S. Dollar is fiat. Account-based U.S. Dollars are electronic money substitutes, just as are all custodial Bitcoin accounts and trade in unconfirmed transactions. These are promises to redeem in dollars or bitcoin respectively.
The dollars that one can hold in one's hand are fiat, just as are the bitcoin that one can spend with one's private keys. As such the term "fiat" alone does not distinguish between the Dollar and Bitcoin. However this distinction was never required before the existence of Bitcoin. Market monies without use value were presumed not to be possible. However there is a material distinction between these two types of money, neither of which have use value. This begs for a new differentiating term.
The Dollar (as all state fiat) differs from Bitcoin in that it depends on monopoly protection for production. It is this prohibition of market competition that allows the state to limit supply and therefore extract seigniorage.
monopoly is a grant of special privilege by the State, reserving a certain area of production to one particular individual or group
The monopoly on production of state fiat is created by anti-counterfeit statute. A unit of the money is considered invalid unless produced by an authorized agent of the state. This is distinct from Bitcoin, as it is produced by market competition and counterfeit is precluded by agreement on a public ledger. Money secured against counterfeit by statute may then reasonably be referred to as "monopoly money" (not to be confused with Monopoly Money), and Bitcoin as "market money". When the face value of fiat is reduced to its production cost it has transitioned to market money.
Commodity money is also market money, as it does not rely on monopoly privilege to restrict its supply. If commodity money supply is too great, it ceases to be a useful money due to the lack of portability. The distinction between commodity money and Bitcoin is obtained from Cryptodynamic Principles. Commodity money supply is controlled through market competition to supply it, as a consequence of its market demand. It is not fiat given the presumption of use value.
Both money and money substitutes constitute currency. Money is sometimes referred to as base money. All monies are subject to lending and therefore necessarily credit expansion (i.e. into money substitutes) and its corresponding fractional reservation.