How is fiat money different from representative money?

Fiat money includes paper money and overvalue coins. So fiat money has the wider range.

The French use the Euro and Canadians use the Canadian dollar (different from the U.S. dollar).

Yes. Prior to adopting the Euro on 2001, the Italian currency was the Lira.

Because usually it is not backed up by any commodity such as gold or silver. While it is possible to have digital currency that is fully backed up by a commodity, most aren't.

Mexican money and us money are very different. for one they both have different names. and they both don't have the same value. Mexican money is worth less then us money.