Ok, lets substitute "bitcoin" in for the words "money" and "currency" and see if your sentences are still true:
MONEY
Bitcoin is any object or record that is generally accepted as payment for goods and services and repayment of debts in a given socio-economic context or country.
Analysis:
Bitcoin is a record, so it passes your "object or record" test.
Bitcoin is generally accepted as payment for goods and services and repayment of debts, so it passes your "payments" test.
Bitcoin is accepted "in a given socio-economic context", so it passes your "socio-economic context or country" test.
Sounds to me like Bitcoin is already a "Money".
CURRENCY
Bitcoin in the most specific use of the word refers to money in any form when in actual use or circulation, as a medium of exchange, especially circulating paper money.
Analysis:
We already established that Bitcoin is a "Money", so it passes your "refers to money in any form" test.
Bitcoin is actually used, so it passes your "actual use or circulation" test.
Bitcoin is used specifically for the purpose of exchanging value, so it passes your "medium of exchange" test.
Bitcoin is not paper money, so it fails the "especially circulating paper money" test.
So the question is:
Does something
have to be paper money to be currency, or is that simply a suggestion?
If it
has to be paper money to be a currency, then bitcoin will never be a currency (since it is an electronic record).
If being a paper money is simply a suggestion, then it sounds like bitcoin is already a "Currency".
There is a slightly different between money and currency but it can make a great difference.
Do you think that bitcoin can become money?
According to the definitions you posted, something can't be a currency unless it is already a money. If you are claiming that it is a currency, then by definition you are also claiming that it is already a money.
Are you suggesting that right now bitcoin is neither a currency nor a money?