That's pretty much the jist of it. There are two primary designs, Garrett and Pratt & Whitney. Garrett uses a gearbox to to slow down the revolutions of the turbine to get them to optimum prop speed. Example: A TFE-331 spin about 41,270 rpm (depending on series) at 100% power, but the prop is spinning at 2000 rpm at 100%. They're what you call "direct drive", which basically means if you spin the prop, you spin the turbine. Consequently though, the gearbox weighs more than the engine does. As for the Pratts, they have a free spinning prop. In layman's terms, the prop is not connected to the engine. Instead the engine (on all models that I can think of right now, i.e. King Airs, except the B100, which has Garretts) is put in backwards, and the exhaust pressure is used to spin a free wheel turbine connected to the prop. In theory, you could start a Pratt, hold the prop during start, and keep it from spinning. Not so with a Garrett.
As for piston airplanes above FL250, yes they do exist. But they all have turbo-chargers, similiar to a car (in principle). A couple of examples would be Cessna 414A, and 421. They are cabin-class piston twins with pressurized cabins, that can go at least to FL250, if not above. Hope this helps.