I think you guys have it pretty well covered regarding the difference in track and suspension (seems more like a TX-L setup). I believe the TX-L and TX had slightly different suspension mounting points but the basic chassis was the same.
I’ve always thought that the “C” does, in fact, stand for “Cross Country”. In the earlier models – say 79, the hood was a different color (all blue) and the sled had a much bigger windshield that was mounted in front of the hood vent. They also had these funky little tool kits down by the foot rests. I think the difference in the 80’s chassis was less obvious.
Based on what I’ve seen in the classifieds, the TX-C’s are much rarer than the TX’s and TX-L’s. I hardly ever see one for sale. That’s a very cool sled. I would grab it in a heartbeat. There just aren’t that many out there. Since you’ve had a TX, I don’t have to tell you that the motors are overachievers. They will wind up in the 9000 range, no problem. Would you run up big miles? No, but on a smooth trail these sleds are still a blast to ride.