All types of drive use belts to transfer power from the engine back to the transmission. The difference is either in the belt travel or the transmission itself.
A Hydrostatic transmission is a transmission that is filled to most of its capacity with Oil. For current models, a 10W-40 oil is being used, but can be serviced with 20W-50. This unit is controlled by some sort of lever that manipulates hydraulic pumps within the transmission. The further in either direction the lever is moved, the harder the pumps operate. These pumps then control the speed at which the drive wheels rotate.
Transmatic drives are similar to a manual shift automobile. To drive, you have to put the unit into gear and release the clutch. It is not necessary to accelerate through gears like a manual car, simply select any gear and operate at that speed. These units use a combination of belts and tensioners to operate the drive system.
For AutoDrive units, the drive system is set up to operate similar to that of an automatic car. An operator simply needs to put a unit into forward or reverse and then press the accelerator until the desired speed is reached. This unit uses a different combination of belts and tensioners that do not require the operator to use a clutch.