Fiat money is not necessarily physical money, it can be of different shapes and forms, for example, pieces, banknotes, spreadsheet entries, liabilities in the central bank's balance sheet to name a few. As you may notice, half of what I mentioned is virtual forms of money. What makes it "fiat money" is the government's decree. They, in effect, say everything we call money must be regarded so, and if you disagree you will find yourself in jail." That is why you consider a piece of paper or a database entry real money, you are obligated to use it as means of payment despite the obvious absurdity of the situation. Money is supposed to be a frame of reference, that is, a means with which to calculate the prices of goods. When governments play with the supply of money, they change these units of measurement and artificially distort the prices. Bitcoin is different because nobody can arbitrarily play with its characteristics, it remains, all the time, a reliable frame of reference.