Commodity money has value other than its use as money. For example, gold can be used as a medium of exchange, but it can also be used for jewellery, gilding, or as an insulator. Simply put, it has other uses.
Commercial money is the part of the currency that is made up of accounting money - debt generated by commercial banks
Fiduciary money is notes and coins available for use in the economy.
Fiat Money are the types of money that are legal tender by government regulation or fiat.