A combat medic (or combat med tech or CMT) is a soldier whose primary role is that of a medic. He or she will be part of the Royal Army Medical Corps. CMTs may be employed anyway from at the front as part of an infantry company or RAC squadron, right through the medical chain back to the field hospitals and beyond. Note that even if employed forward, a CMT will not be employed as an infantryman or armoured fighting vehicle crewman as his or her role is specifically to provide medical cover and not to fight (except in self defence or to defend his/her patients).
A team medic is a non-medical soldier who has been trained to give some medical care. This is really a bit more like advanced first aid. The team medics role is principally that of an infantryman/AFV crewman, etc. but he has the additional training to be able to provide some emergency medical treatment.