A monetary system is made up of all the different kinds of money circulating in a country or groups of countries e.g. the EU.
We remember the most famous
Gold standard
paper monetary system
The gold standard ceased at the beginning of the 1st World War when a lot of countries were compelled to issue a great amount of banknotes in order to cover the cost of the war. Additional revenues and the issue of bonds were not enough. So governments were forced to declare the inconvertibility of banknotes. These became the legal money.