Anything that is easily used as a medium of exchange in settling a trade is called money. Earlier demanded commodities like salt, rice wheat, weapons, livestock was used as money, it was called barter exchange. After that metallic money like gold, silver, copper come into existence. They were quiet popular. Soon this money was found inconvenient as well as dangerous to carry, so replaced by paper currency. Every country prints its own fiat currency as per their policy; generally these currencies are printed and controlled by the central bank of that country. After economic revolution paper money is accompanies by credit money, plastic money etc. The latest form of Digital money (bitcoin) gets introduced in the year 2009. Purpose of all forms of money is to make the trade simple and easy.
It is true that many things were used as a medium of exchange but it was not until coinage was invented that we got money, before you needed to look at the quality of the metals and most of the time the precious metals were in odd forms, coinage solved those issues and made exchanges easier, that was the first time we actually got money but fiat is not money even if governments want you to accept it as such since it does not fit the full definition of money.