FIAT money is a currency issued by a government that is not backed by a physical commodity but instead is backed by the issuing government.
The U.S. dollar, the Yen, and the Euro are good examples of FIAT currencies.
Stablecoins are a type of cryptocurrency pegged to the value of a fiat currency and are designed to maintain the price of it. Stablecoins can be backed by different types of assets (cryptocurrencies or FIAT) and even by algorithms (algorithmic stablecoins).
USDC, USDT, and DAI are good examples of stablecoins.