A rotary cutter "bush hog" usually has a single heavy gear box, with a pair of heavy blades (3/8"-1/2" thick), and is used for mowing thick tall weeds and small brush along roadways, etc. It is either three point mounted, or pulled on the drawbar. The cut is effective but rough.
A finish mower is very similar to a belly mower on a garden tractor, having multiple spindles and lighter blades (3/16" -1/4" thick), except that it is mounted behind the tractor on its three point hitch. It is primarily used for mowing larger grassy areas, such as ball diamonds, etc. Smooth even cut.
Both types are available as bat-wing style, but that is a whole other topic.