Is there a difference between a bone infection and an abscess?

Yes. An abscess does not necessarily/usually involve bone. Bone infection does not necessarily cause an abscess. Abscess is a walled off pocket of dead tissue (pus) somewhere in the body.
Yes. An abscess is an infection. It can occur in bone as well as in any soft tissue. An abscess in bone may be harder to treat and drain than an abscess in soft tissue, but they are quite similar.