There's a lot of distinct differences that could be drawn between the two.
1. Fiat can be created from thin air; cryptocurrencies has a set amount of coins to be mined/acquired.
2. Inflationary (fiat) vs Deflationary (cryptocurrency)
3. Region-restricted purchases (fiat); shopping with no borders (cryptocurrency)
4. Requires an intermediary to store money (fiat); you're your own bank (crypto)
These are some of the things that differ crypto from fiat. There's a lot more aside from those things but that's just what I thought off the top of my head.
Nice said. But on important fact for me is the point number 1. A lot of bad things happens when you print money and this creates inflation and everyone is doomed. With crypto you have to mine to create more and with the invention of blockchain you can watch what "they" are doing. If a Government creates a crypto-coin you will be able to detect easily if they are creating more and if they needed more (the initial setup is a fixed number of coins) they have to update the blockchain (create a hardfork). So more control and transparency for all.