Agreed. If you are only hearing it during patient reports to the hospital, then it is something to do with the patient's condition. Most systems that utilise such codes use a "priority code" system, with priority-one being a patient with immediately life threatening and unstable condition, down through priority-5, being a routine inter-facility transfer of a stable, non-acute patient. Those codes, of course, have nothing to do with telling what the specific problem is, just how serious it is, so the hospital can decide what preparations must be made for the patient.
I would suspect that Austin-Travis County EMS, who is fond of doing their own thing completely different from the rest of the EMS world, just made up their own codes. They could be the same as the priority codes, or they may mean a specific type of illness. For example, category C may mean a cardiac problem, or it could just be the same thing as a priority 3 (c=3), which would be an emergency patient who is in no immediately threatening distress. I know some EMS systems up north utilise priority codes Alpha thrugh Echo, with Echo being the highest priority instead of the lowest, so that is also a possibility. It could go either direction.
Yeah, you can ask somebody at A/TC and find out the easy way. But it might be more fun to simply listen to a lot of those patient reports, compare the patient features, and come to your own conclusion first. Such detective work is the most fun part of the scanning hobby. One big clue -- even if you are not medically inclined -- would be whether or not you hear sirens in the background or not. If so, then Category Charlie is hot stuff. If not, then Category Charlie is low down on the priority list. Although, a heart attack, though serious, is still usually transported without sirens. Good luck.