Fiat money (or fiat currency) is a currency that a government has declared to be legal tender. Cryptocurrency is not legal tender and not backed by a government.
Fiat roughly means, “let it be done.” Cryptocurrency implies, “a decentralized and digital medium of exchange governed by cryptography.” Both are currencies, but there are some notable differences:
Fiat currency is “legal tender” backed by a “central government.” It can take the form of physical dollars (for example paper Federal Reserve notes), or it can be represented electronically, such as with bank credit. The government controls the supply and you can pay your taxes with it.
Cryptocurrency is not “legal tender” and it is not backed by a central government or bank (it is decentralized and global). Its form is more like bank credit sans the bank (in that it is represented digitally, but not backed by a bank or government). An algorithm controls the supply and you can’t pay your taxes with it (instead you have to pay taxes on it).
Otherwise, there is no intrinsic difference. Both fiat currency and cryptocurrency can be called money or currency, both are mediums of exchange that are used to store and transfer value, both can be used to purchases goods and services, both have their value governed by supply, demand, work, scarcity, and other economic factors, both have their value affected by the quality of the system surrounding it, both can be traded on exchanges, etc.
Cryptocurrency, gold, a bundle of wool, and a dollar are all stores of value and all have exchange value. Some value stores like the wool and gold have use value, some like fiat currency and cryptocurrency are meant to be a store of value and medium of exchange only.
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