Is there a difference?  Some people like to be hyper-technical, while others are fine with using them interchangeably. It really boils down to this (for all you word mincers):

Co-Sleep-

Baby is in the room with you.  Baby has their crib in your room, a co-sleeper in your room, or is in bed with you, in your room.

Bed sharing-

Baby is in bed with you.  That's it.