I'm not familiar with this term "medical trainer." In the field of orthopedics and rehabilitation, I interact with personal trainers, athletic trainers, and physical therapy assistants, and physical therapists. I am a physical therapist myself. There may be a subset of personal trainers or that have gone through certification courses that give them some extra knowledge base on how to strengthen those with medical injuries. There are no nationally recognized, by government or insurance, that I can speak of that designates someone as a "medical trainer." I would do much more research into anyone that tells you otherwise.
From what I understand, a "trainer" helps create and execute exercise programs for people hoping to improve their physical fitness. As a physician, I've never interacted with or heard the term "medical trainer."