sound dampening and sound deadening are usually referring to the same thing. Preventing the vibration of something which is exposed to sound waves. If the surface cant vibrate, it can't generate sound. Dynamat is an example of a sound damping material. It can be effective on the side panels of computer cases which will vibrate from the fan noises. Sound proofing is usually the use of insulation (of some type) to absorb the sound and keep it from escaping. Soundproofing is not usually used because it requires thick blankets of something to absorb the noise.