Currencies are just another asset with some additional properties. The most important additional property is that people are willing to exchange it for any other asset. The point at which an asset crosses over to the currency or medium of exchange is elusive.
The paradox is, a modern society needs currency in order to function (barter doesn’t work because of the double coincidence of wants), however, determining when to add/subtract currency (i.e. the money supply) from the world is imperfect. So the question is, how do you do this where all participants are treated the same?
The US dollar’s money supply is managed via lending. That is, currency is lent into existence. This methodology is extremely flexible through the use of inflation and generally depends upon prices going up, however, it’s not a panacea. If loans are not collateralized “fairly” then a bank's special ability to create loans in this closed system can harm everyone that holds dollars.
Currently, the Bitcoin money supply is managed through mining up to a finite number of Bitcoins. This is considered deflationary and has the potential downside of everyone holding Bitcoins and prices going down.
Bitcoin, imho, is not a currency because it isn’t used as a medium of exchange, yet or maybe never. However, it is a store of value (not saying it’s a good or bad store of value) with a limited supply. In time, we’ll learn whether that in and of itself is useful and therefore justifies the price or just a speculative bubble.