Felt is made from matted or compressed fibres - usually but not always wool. Batting is the material used to put in a quilt sandwich specifically . So a piece of felt could be used as batting (but I wouldn't recommend it for the reason Patrice gave)! :mrgreen:
I think the difference is that felt is defined by how it is made (see above) and batting as how it is used. Any kind of soft stuff could serve as batting. :-D