I'll use my tractor as an example. My transmission has a main shift with 4 synchronized gears, a high / low range shift, a shuttle shift, and a clutch pedal. The 4 main gears with the high and low range gives 8 different speeds or gear ratios. The shuttle has three positions; forward, neutral, and reverse. So, I use the main shift and the range shift to select one of 8 speeds and then set the shuttle to forward, neutral, or reverse.
OK, because I have 4 synchronized gears in the main shift I can shift between these 4 gears while the tractor is moving, using the clutch pedal. I cannot however shift between high and low range while the tractor is moving because those gears are not synchronized on my tractor.
With a synchronous shuttle you use the clutch and change the shuttle position, while moving if you like.
My tractor has something called a hydraulic shuttle, it uses a wet clutch. If I want I can change the shuttle position without clutching. This is especially nice when doing a lot of repetitive forward/reverse loader work. The wet clutch is also supposedly more durable and smoother to operate than a dry clutch.
This might be what you are referring to as a power shuttle, although there is also something called power shift, where one can change speeds/gear ratios without clutching.
Which tractor model/setup are you considering?