Money in that context has two kinds of common usage:
money noun 1 A current medium of exchange in the form of coins and banknotes; coins and banknotes collectively. ‘I counted the money before putting it in my wallet’ 1.2 The assets, property, and resources owned by someone or something; wealth. ‘the college is very short of money’ - lexico
Money is an economic unit that functions as a generally recognized medium of exchange for transactional purposes in an economy. - investopedia
Currency, on the other hand, relates a lot more strongly to the underlying physical expression of money:
currency noun 1 A system of money in general use in a particular country. ‘the dollar was a strong currency’ - lexico
Currency is a medium of exchange for goods and services. - investopedia
So money is a more abstract concept, and currency more concrete. You can talk about money without referencing notes or coins, but you can't talk about currency without referencing them.