From a quick Google, looks to me like a THC uses a proximity sensor to detect the material. The thc will adjust the height to a set distance and maintain that distance in real time as it moves. Vey useful of the material is not flat.

If you're only going to be cutting flat material, a stepper motor would certainly be cheape than a THC controller, just not as cool.

Plenty of info and videos on THC when I google it.