Cute. It is true that the definitions according to Webster are similar. However, Merriam-Webster to the best of my knowedge has never built a shock absorber or designed a suspension system. There is such a thing as a difference between literal definition and contextual. In this case the contextual definitions are not the same.
Dampening refers to the musical technique of muting an instrument while playing it, or soon after, before it has lost its sustain (stopped ringing). It can be used on a wide variety of string and percussion instruments. This may be done with a mute.
Dampening also generally refers to the presence of water in trace amounts. It is found in several different forms, which can cause rot in wood or other organic material, corrosion in metals, and electrical short circuits.
Damping is any effect, either deliberately engendered or inherent to a system, that tends to reduce the amplitude of oscillations of an oscillatory system.
In physics and engineering, damping is mathematically modelled as a force with magnitude proportional to that of the velocity of the object but opposite in direction to it. Thus, for a simple mechanical damper, the force F is related to the velocity v by
where B is the damper constant.
This relationship is perfectly analogous to electrical resistance. See Ohm's law.
http://en.wikipedia.org/wiki/Damping
Feel free though to keep using the incorrect words and being proud to do so. Just trying to help you out.