Your quoted defintions suck don't they.  

Money is "monnaie", coming from "Juno Moneta":

https://en.wikipedia.org/wiki/Moneta

This word has a little bit of history pointing towards a "State" interpretation, which depending on what that means to you it might suggest bitcoin is not really money.  Some have certainly claimed so and this is a defensible claim in the context of it not being coinage of a Romanesque State-claiming apparatus.  

On the other hand, in common English money has taken more of a general usage, (i.e. the money shot, "that was money", "what's up money?", etc.)  and as such is more often taken to mean any exchange commodity.  Because any and all things could be used as exchange commodities, we could therefore argue that bitcoin is an effective money.  Context is important here going between the different meanings.  

As to currency, this implies a "running" or a flow, meaning that many people use it.  Cigarettes are therefore currency in some places but not in others.  Bitcoin is currency insomuch as (if) there is a large community of people using it as an exchange commodity.