Is Bitcoin a means of storage of wealth, or is it a payment system?
If Bitcoin has to be a currency, it certainly must be both.
The US dollar is a currency and is neither.
If USdollar is currency, it must be both. For the record, there is nothing like a pure currency. USD is definitelly getting less and less currency. Bitcoin is getting more and more currency.
But honestly there is nothing to debate over. Definition of money is:
#1 a medium of exchange
#2 a unit of account
#3 a store of value
#4 standard of deferred payment.
(money is all 4 points at once)
So the logical implication is that if bitcoin (or anything else) has to be a currency, it must be a storage of value and payment system=medium of exchange. Another logical implication is that if you believe that USD does not fulfill all 4 points above, then you do not believe it is a currency. (Maybe you have your own definition what currency is, but then we really have a problem.)
Last remark: far the biggest problem for bitcoin will be #2; everyone thinks in USD or fiat even when using bitcoin. I pay people in btc always based on exchange rate. Their salary is 4K USD, not 10 BTC.
Still all this is trying.
Maybe the internet started as an experiment (or still is) but there is no categorical definition what it is.
We just have some protocolls living in it like smtp or html.
Bitcoin is next such a protocol / experiment. Could be that the biggest experiment to us is yet to find out what it is?
Best answer: it is a full new category and we only can project some of it to lower dimensions we can better understand because we can touch it.