What is the difference between Commodity Money and Fiat Money?

Fiat Money is anything which is proclaimed by law as a medium of exchange. It serves as money by order or authority of the government. Nobody can deny its acceptance as a medium of exchange. For example, paper notes and currency are Fiat Money because they are accepted as a medium of exchange by the law. While, Fiduciary Money refers to anything that is accepted as a medium of exchange by the trust between the payer and the payee. For example, in modern days, cheques are Fiduciary Money because they are accepted as medium of exchange by trust and not by the order of government.
Similarly, Commodity Money is a kind of Fiduciary Money because they are accepted as medium of exchange by the trust between both the parties. Also, the value of Fiat Money is specified by the government while the value of Commodity Money is the value of the material it is made up of.