What are the differences between an orthopedic surgeon and an oral & maxillofacial surgeon?

Different. Orthopedist works on musculoskeletal system: bone, joint, ligament, nerve, muscle, tendon. Oral surgeon works on oral cavity and facial issues of bone & soft tissue that relate to this.
Jaw & facial surgeon. Oral and maxillofacial surgeons care for patients with problem wisdom teeth, facial pain, and misaligned jaws. They treat accident victims suffering facial injuries, place dental implants, care for patients with oral cancer, tumors and cysts of the jaws, and perform facial cosmetic surgery.
Different. Orthopedic surgery is the branch of surgery concerned with conditions involving the musculoskeletal system, oral and maxillofacial surgery is surgery to treat many diseases, injuries and defects in the head, neck, face, jaws and the hard and soft tissues of the oral (mouth) and maxillofacial (jaws and face) region.