Both arts kick with the ball of the foot.
About thrusting with your heel. Ever thought what would happen if you missed and then stepped down? Smack, uppercut to face cause you would have your face bent down a little. Perfect degree to throw the showel hook. 45 degree.
Anyone these days avoid using the heel as your momentum/center of gravity would be in the opponent. So if you hit and he suddenly moved to the side. You have your side open to him now.
Still, hitting with your heel would create a larger effect than just using the ball of the foot as the heel is larger and more force can be concentrated on it.
The last time I saw a heel delievered was to the face, not the stomach. If it was stomach, I think he'd use the ball of the foot. Too much risk with heel.
On the second note, I could be totally wrong. Maybe it's better to hit with your heel but personally, I'd never try it in a fight, I don't wanna get hurt because of some theory. Just use what you feel comfortable.
How is it delivered? Well, what I have seen is Karate's kicks ends with the foot being drawn back to the standing knee position while MT just thrust out and take down the leg to the ground. The same principle of pulling up your knee and then deliver is used for both arts.