Medical Corpsmen (medics) in the US military today do not have MD diplomas-- they are not physicians. They are more directly trained to the level of Emergency Medical Technicians, and in fact, at least in the Army, most have EMT training and certification. As to "Engineers", historically most military activities build things (e.g. bridges, roads, fortifications) and break things (e.g. ditto). Thus, military construction personnel have traditionally been referred to as "Engineers", which term pretty much supplanted the previous term "pioneers" in this context. While most enlisted personnel in the Engineering units do not have degrees in engineering, these units are normally led by officers who do have such specialized training. The study of military engineering was so important to the US military that this field was the primary field of instruction following the establishment of the West Point Military Academy.