I think the MT bag is longer and perhaps thinner, it still is probably the same weight as a "heavy bag", but I think it is more stretched out. The "heavy bags" that I used and have had over the years were shorter and fatter. The MT bags being longer allowed for the low line kicking techniques. Where as the "heavy bags' were heavier on top to represent the upper body.
Back before MMA and MT were so prevalent, I worked out briefly at a karate (kickboxing) school (early 80's) and I remember any karate school I trained at having a "heavy bag" and at Greek's school he had a "banana" bag that was/is the MT type bag today, along with the standard "heavy bags" to do bag work on. It was unusual at the time.
Yeah those banana bags. Never actually seen up front, only in pictures. To be honest, it has never really occurred to me to think about heavy bags any differently. I don't really go into detail with sort of thing. If it is made by Intel or AMD I do lol. With bag work I have always had a punching bias in a workout. So I guess my thoughts on types of bags pretty lived there.