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.
Maybe not. You can use a non-currency money to pay for something, see my example above about paying a tailor with a check.
Most likely, Bitcoins are forms of money transfer, not a currency, though the process is easy and anonymous enough to treat them as such.