People seem to be a bit over-prescriptive here about the definitions and uses of money vs currency. They are partial synonyms and at some points one may be able to draw a distinction - othertimes not. Currency also has some wider/alternative definitions as well.
IN ECONOMICS
Conceptually, from an economics perspective, there are three key properties of something that is money: it is a medium of exchange, a store of value and a unit of account. These are all somewhat inter-related - liquidity in exchange, and consistency in pricing between goods and over time are mutually reinforcing.
There are common properties to things that work successfully as money that they are likely to share to a greater or lesser degree: to be light, discrete, robust, and be in sufficient but stable supply.
This is why at various time and places different things have achieved currency as money: shells, commodities, promissary notes, cigarettes, etc.
[[ ADDED ]] Central banks and economists distinguish between "narrow money" (coins and notes and other banks deposits and the central bank) and various definitions of "broad money" adding on other non-physical money (retail bank deposits, bank-issued noted and bonds, inter-bank lending etc).
IN ETYMOLOGY
"Money" derives ultimately from the Latin name for a mint where coins were made while "Currency" derives from the Latin for "running", "moving", "in circulation". But "money" no longers refers exclusively to physical coins.
IN LANGUAGE
In terms of practical use of language:
"Money" by itself usually refers to a form of money that is relevant to the conversation at hanf: E.g. "Do you have enough money?" is a question about whether you have sufficiente funds to hand in a form you can use. The meaning changes if I am standing infront of a carpark ticket machine that only takes coins (money = coins), signing on the dotted line for a new car (money = content of current account), or contemplating buying a new car soon (money = easily realisable savings).
Even "cash", which usually refers to physical notes & coins is sometimes used differently in, say, company accounts. "Cash-back" at the supermarket EPOS terminal means notes; "Cash-back" in a sales promotion probably means a cheque.
"Currency" can be descriptive - something can have the property of "currency" - as well as being a thing that circulates in the economy. It is more frequently used when referring to a specific unit of money in the abstract - Dollars, Sterling, Euros etc - particularly in a comparative context - e.g. international currency exchange. So I might consider the USD a "hard currency" or go to the Bureau de Change to change money into a different currency.
But I can jam most of these words in to most phrases without very much risk of being misunderstood, even if it sounds a bit off to a native speaker.