As the name suggests, a dentist treats teeth, implants and dental prostheses, treating gums, badly aligned teeth and oral pathologies.
While they may treat some of the same aspects as a dentist, a maxillofacial surgeon is specialised in maxillary surgery which includes complicated extractions, bone grafts and dental implants.
In terms of training, a maxillofacial surgeon needs to be licensed in medicine and surgery prior to specialising in maxillofacial surgery complete with a residency in a hospital. A dentist may be a doctor but does not have to be, as there is now a degree in odontology that is independent of medicine.