After the 500th time reading someone complain about the clomping foot traffic noise of the tenants upstairs, and the 1000th response from a well-meaning someone else advising them to install acoustic tile, I've gotta post something that will hopefully get Googled for the next poor shnook who asks about it. I don't have an architectural acoustics degree but this is something I learned in the trenches, building recording studios.
There are two basic types of noise control: one that alters the acoustics inside a room (absorption) and one that contains that noise and keeps it from invading neighboring spaces (transmission). The respective technical approaches are about as similar as frying a hamburger and paper training a puppy. In other words, different.