As you go from standard to medium to heavy duty, five things get heavier and stronger on the cutter.
1. The gearbox guts get stronger and get a higher hp rating, so the gears don't break when the blades smash into a Stegasaurus skull.
2. The top deck gets thicker (in gauge), to prevent the deck from denting and cracking when bigger and bigger rocks, logs, and skull fragments are recirculating around at 18,000 fps under the deck.
3. The side skirts get thicker, for the same reason.
4. The blades get wider and thicker (but not longer).
5. The bracing structure on the top of the deck gets heavier duty.
These increases in thickness and strength are what allow a medium to cut a 2" stem, for example, instead of a 1". Actually, you can probably cut the 2" stem with the standard duty cutter, but if you do so frequently, the decks, skirts, blades and/or gearbox will give out a lot sooner than on the medium duty.
The problem is, there is not an industry standard as to what dimensions and thickness and strength of structure constitute standard, medium and heavy duty. One manufacturer's standard duty may be as strong in all five categories as another manufacturers so-called medium duty. That is very common. For example, the Midwest medium duty cutter linked above seems to have about the same thicknesses as the Woods standard duty (just going from memory).
Therefore, you must carefully compare the spec sheets of the cutters you are considering. Then there is build quality. Some cutters have thick decks and side skirts, but they are held together by cheap spot welds.
You get what you pay for. There is no free lunch.