I'll explain properly since everything on here is confused :)
Currency is a descriptive, not definitive, term.
It simply means
"anything that is, at present, popularly used as payment and will be widely and generally taken as payment"
That's all it means.
So for example, within Disneyland, those DisneyBucks pieces of paper, you could indeed describe as currency. It would be reasonable to state "DisneyBucks are currency within Disneyland, but really you can't use them much if at all outside Disneyland."
It would be perfectly reasonable to state "US Dollars are, of course, currency anywhere in the US, and also in certain developing countries. In say France or Australia, US Dollars are not currency, they are not of course popularly used as payment and will not be widely and generally taken as payment."
So that's all "currency" is.
At different times "government paper money" has been currency, "shells" have been currency, "military scrip" has been currency, "private banking notes" have been currency, and so on.
Let's say there was some sudden financial cataclysm in the US (or any country, just the US for example) and the US government money suddenly hyperinflated and became comic, nobody would accept it for payment or exchange. Then, we would say "Wow, look what's happening in the US, the UUSD is not currency anymore."
Here's a great example. In fact in many situations the US one hundred dollar bill is not currency currently.
As anyone who, uh, launders huge amounts of paper money or is a major drug lord will tell you, large-denomination bills are no good: the only thing that is current ("that will be widely and generally accepted") are smaller-denomination bills.
Over in Europe there's a 500 Euro bill; I would say it's not really currency; generally folks won't accept it. "Currency" means widely/universally accepted as payment (in the area/time in question), I've found 500 Euro bills are really not currency.
So from the question, "Currency, on the other hand, is the "promissory note or coin"" That's totally and completely wrong on many levels. (A "coin" can just be a promissory note, or, it can be simply a token, or it can be literally some bullion.) Currency may or may not have any connection, at all, to "promissory notes" - again apparently "shells" were a popular currency in some milieu. On the other hand no-one actually knows what the US Dollar is (it is explicitly deliberately undefined, other than that the government there asserts "it" can be used for tax payments), but US Dollars (excepting large denomination notes) are absolutely current.
Note that "current" is just used in the normal meaning of the word...
So for example, it's totally normal to say "K-Pop music is current!" simply meaning it's popular, whereas jazz say is not really current today.
"Current" means nothing more than "currently popular".
Regarding "What is money" ? This is simply definitional. Various experts will give you their definitions of what they, in their academic writing, consider money.
It's completely normal to consider only gold "actually money". (So, the three or four most powerful figures in fiscal matters of the current era - think this.) Other say money is a "medium of exchange". OK. Other say money is "a function of the current social power structure", again perfectly reasonable (I defy anyone to "not need" USD or Euros). And so on.
It is utterly, utterly, pointless arguing about "what is money", because it's purely definitional.
(Consider say the question "What is a 'Symphony'?" I don't know or care, but various musicologists over the centuries, and today, would have various and different stated definitions of what a Symphony is. There is utterly no "answer" to "What is a Symphony"; it's just a term used by academics and others, and all you can do is write down the various meanings stated by each of those persons.)
So "money" is just definitional; it's utterly pointless/meaningless to "argue" about "which" definition you support or whatever.
"Currency" is a factual thing.
If I told you "US Dollar notes are currency in Anguilla", that is an observable, checkable, fact. I could literally take you there (ideally checking in to Cap Juluca!) and one could observe and check that US Dollar notes widely/universally accepted as payment/exchange.
So that's it.