It might help to tell us what tractor you have. You said a 35HP kubota.....but your avatar lists a 16hp
B7100.
AS to the term, for all-intents-and-purposes, rotary cutter and bushhog are one in the same. While technically though....bushhog is the brand, and rotary cutter is what it is.
No different than calling
and adjustable wrench a crescent wrench
slip joint pliers being called channelocks
locking pliers being called vice grips
hex keys being called allen wrenches
etc etc.
Regarding light vs medium vs heavy duty.....
They will all clip pasture grass well. Meduim and heavy duty cutters are made with bigger heavier blades and gearboxes, and thicker metal. So they will stand up to occasionally hitting a rock, or mowing over some tree saplings alot better. But they cost more....
The horsepower required to run the cutter dont care weather its a heavy duty cutter with thicker metal, or a light cutter. What you are cutting and how fast you go is gonna determine the HP required.
Reason why I ask what tractor you have, is because you are asking about a pretty broad range of cutters. And in a pretty broad range of tractor sizes just saying a 35HP kubota. A light 5' cutter can be down a round 450-500 pounds. And a heavy 6' can go north of 1400 pounds. And Your could be a 2200# 2wd machine, or you could have a 3400# 4wd machine with loader.
A medium duty ~900-1000# cutter on the lighter end of the 35hp tractors isnt gonna work well without a front loader, or front weights. Where as it would be handled just find on the heavy end of kubotas 35hp tractors.