The word comes from the Latin for "let it be": money is worth what it is declared to be worth, not what the metal weighs. Every modern currency works this way.
Why the word comes up when exchanging
It is shorter than the list. "Fiat deposit" means topping up by card or cash, "fiat withdrawal" means receiving hryvnia in an account. Exchange directions split into crypto to crypto and crypto to fiat, and the second is always harder: a bank takes part, with its own rules and its own timings.
How fiat differs in practice
In reversibility. A mistaken bank transfer can be disputed, a mistaken blockchain transfer cannot.
Why fiat directions take longer
Because a third party appears: the bank. It has its own working hours, its own limits on incoming payments and its own checks. The crypto side of an exchange takes minutes, the banking side can take hours.
For the same reason fiat directions usually carry amount limits that crypto to crypto does not have: they are set by the payment system, not by the exchange service.
Cash is fiat too
Exchanging for cash removes the banking side entirely: no crediting, no questions about the payment reference, no waiting. In its place comes a meeting at an office and its own constraints, opening hours and city.
Read more: How to declare income from cryptocurrency