What is the difference between an overdamper and an underdamper?
Overdamper: An earlier design employed by upright piano builders in the 19th century where the dampers are placed above the piano hammers - Even in the 21st century these types of pianos are still around. The main disadvantage is that for the poor piano tuner as they are hard to work on and for the pianist, they do not damp the sound as well as an underdamper. You can tell these as they are old and tall pianos and when you look inside you will see a wooden bar on top of the action.
Underdamper: This was main change in the design of pianos in the late 19th century with most successful piano makers. The dampers are below the hammers.