Stomatology is the science of the mouth and its diseases. It can be studied, but not practiced. It is the science of dentistry, not the medicine of it.
Dentistry is either the profession, or the science dealing with the prevention and treatment of diseases and malformations of the teeth, gums, and oral cavity. It canbe studied and practiced.
Stomatology is not a commonly used word. One does not visit a stomatologist. One visits a dentist.