There are three basic systems in use.
1. Clutch/brake. Much as you described, common in plant and some tanks, particularly Russian but also Valentine.
2. Controlled differential. Like it says, a differential controlled by brakes, one each side. Quite common, though wasteful of power. Used by Stuart, Sherman, FV430 series etc.
3. Regenerative. This is a more complex system often known as triple differential. This uses a train of gears, often epicyclics and controlled by brakes. Little power is wasted because each track is driven but at a different speed, the ratio varying with the selected gear. Most common is the Merritt Brown as used in Churchill, Cromwell, Centurion etc.
There are and have been other systems in use, track warping, Wilson epicyclic steering units etc etc but they are all variations on a theme.