I'm not an expert on this subject. But I think I can clear up some of the confusion. The basic difference between the GST and the HST is not whether they have gears or not, it's how they couple the engine to the transmission gear sets. Both of them use gear sets. The gear sets are coupled with either a conventional clutch/pressure plate combination in the case of GST or with a variable displacement hydraulic pump running a fixed displacement hydraulic motor in the case of the HST.
The GST is basically a conventional clutch/pressure plate coupling, but you do not have to depress the clutch petal to shift from forward to reverse, or to change gears. There are electrically operated servos that do the clutching for you. You have a lever that allows you to select forward or reverse, and you can move instantly from forward to reverse using this lever. There is another lever that selects the gear desired. Youn can shift on the fly from one speed range to another. You have a clutch petal that works like a regular clutch for idling in gear, or inching forward/back.
The hydrostat trans as used in the Kubotas consists of a variable displacement hydraulic pump plumbed to a fixed displacement hydraulic motor which is in turn coupled to a conventional 3 speed gear trans. You control the displacement of the hydraulic pump and the direction of hydraulic fluid flow with the foot petal. This gives you the ability to idle in gear without moving and instant reverse. But you cannot change from one speed range to another on the fly, you must stop the tractor to change speed ranges via the 3 speed gear trans. You also have up to 20% loss of hp thru the hydraulic pump/motor.
With a conventional gear trans. (not GST) you have to depress the clutch, stop the tractor, and then shift to the gear wanted. A shuttle shift trans adds a lever to the standard gear trans. that allows you to go directly from forward to reverse without using the normal gear shift lever. These were originally developed for loader work. I think some of the shuttle shift trans also have a servo to operate the clutch when using the shuttle shift, but I'm not sure.
HTH
Dave Perry aka karmakanic