Most people look at a dollar bill in there pocket and think they have money. By many accounts they do. However, if you look at that dollar bill, it does not claim to be money, it claims to be a Federal Reserve Note, good for debts public and private.
To even further back the concept of money as just an idea, most of our money is digital. How many times do you actually use the fiat paper money anymore. We use the internet to setup direct transfers, bill pay and use credit and debit cards to transfer most of our money around.
From Miriam-Webster dictionary:
1mon·eynoun, often attributive \ˈmə-nē\
plural moneys or mon·ies
Definition of MONEY
a : wealth reckoned in terms of moneyb : an amount of moneyc plural : sums of money : funds
: a form or denomination of coin or paper money
a : the first, second, and third place winners (as in a horse or dog race) —usually used in the phrases in the money orout of the moneyb : prize money <his horse took third money>
a : persons or interests possessing or controlling great wealthb : a position of wealth <born into money>