From wiki,
Money
Money is any object or record that is generally accepted as payment for goods and services and repayment of debts in a given country or socio-economic context.[1][2][3] The main functions of money are distinguished as: a medium of exchange; a unit of account; a store of value; and, occasionally in the past, a standard of deferred payment.[4][5] Any kind of object or secure verifiable record that fulfills these functions can serve as money.
Currency
In economics, currency refers to a generally accepted medium of exchange. These are usually the coins and banknotes of a particular government, which comprise the physical aspects of a nation's money supply. The other part of a nation's money supply consists of bank deposits (sometimes called deposit money), ownership of which can be transferred by means of cheques, debit cards, or other forms of money transfer. Deposit money and currency are money in the sense that both are acceptable as a means of payment.
So from this I'd gather that currency is the actual thing used for exchange, whereas money is the abstract. I could give you 1 BTC for a stick of gum, and that'd be a use of it as a currency. However if I just give you a wallet.dat that contained 1 BTC, that would be using the wallet.dat as money. I think.