Band and hobby band is kind of backwards from how we always looked at it.
Any group of people "Banding" together to do anything is a band. Remember Band of Brothers? No musicians getting paid there....

So any guys jamming in a basement can be considered a band.
We split the hair on the term "Gigging" A gigging band is a different animal than just a band. It means your working.
Why not let everyone form a band if they want? Just like anyone can form a sports team, you don't need to be getting paid to play baseball to be on a team.
Then, if anyone says they are in a band you just ask "are you gigging yet?" and the answer will be yes or no but they are still a band.
Just my thoughts on it.
-eSmith.