This is what my Class III looks like:
It's the kind that connects to the subframe under the back of the car.
I would call that one a universal fit, and needs to have holes drilled. The two I have both bolt in using the factory holes and bolts, with no holes needed to be drilled.
It's definitely just for Eagles (and maybe Concords/Hornets), but I think the only holes I drilled were to insert nuts because captured nuts weren't there.
It's definitely a Class III, and the Class II factory hitches didn't bolt back to the subframe. I believe it's really a Draw-Tite manufactured item sold by U-Haul.
There were certainly other manufacturers that made them differently, but I don't know of them offhand.