I know I am late to this discussion, and hate to go back to the beginning, but I have never seen an "official" guidline to classify these tractors. We have the ability to define that now right here on TBN. (those that dont follow these threads will just be out of the know).
My view on this, as it relates to todays products:
Garden tractor, is a heavier duty lawn tractor that has ability to add PTO driven equiment, other than mowing deck, (usually by belts off front of engine, but equipped with a clutch/pully arrangement to allow say, a rear mounted roto tiller. Normall on fabricated (stamped or welded, as opposed to cast iron) frame.
Sub Compact is a still heavier duty Garden tractor, with permanantly installed PTO and 3 point hitch but typically will still on fabricated frame connecting the engine, transmission and/or rear axle/transaxle together.
CUT to me is a small tractor where the engine, transmission and rear axle make the backbone of the tractor, generally cast iron, other than weldments used possibly to attach the front axle, loader, ROPS etc. Generally tractors that fall under the Untility tractors that I believe have industry accepted classificaitons, although I confess I do not remember the break points on those.
Really an of these could be built with gas or diesel engines, to me that alone wouldn't change the classification.