The opposite of commodity money is fiat currency, also known as fiat money. The distinction between fiat money and commodity money is one of intrinsic value. Commodity money has historically had intrinsic value derived from the materials it is made of, such as gold and silver coins. Fiat money, on the other hand, has no intrinsic value; it is essentially a promise from a government or central bank that the currency can be exchanged for goods worth their face value.
The pound sterling, euro, and US dollar are all examples of fiat currencies. In fact, very few world currencies are true commodity currencies, and the vast majority are some form of fiat money.