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A monetary system is a set of policy tools and institutions through which a government provides money and controls the money supply in an economy.
Commodity money system 
A commodity money system is a monetary system such as the gold standard in which a commodity such as gold is made the unit of value and physically used as money, any other money, such as paper notes, being theoretically convertible to it on demand. An historical alternative which was rejected in the Twentieth Century was bimetallism, also called the "double standard", under which both gold and silver were legal tender.
Fiat money 
The alternative to a commodity money system is fiat money which is defined by a central bank and government law, or "fiat", which defines legal tender. Typically fiat money is paper currency or base metal coinage, but can also be simply data such as bank balances and records of credit or debit card purchases.
See also 
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