The primary difference between commodity money and fiat money is that

Commodity money has intrinsic value whereas the fiat money does not have intrinsic value

Explanation:

Commodity market is the market which have the virtual or physical market place for trading, buying and selling of primary or raw materials. Presently, about 50 major commodity markets worldwide. And this market has intrinsic value, which means that the commodity has value though not used as money.

Fiat money is the currency created as money, usually through government regulation, and has no intrinsic value.

Therefore, the primary value is that the commodity market has intrinsic values whereas the fiat currency does not have.