Damping is using a material or device to take the energy out of vibration by transferring it to heat. The shock absorber on a car forces oil or gas through small passages. That takes energy, which becomes heat, in the process damping suspension movement. Materials like sorbothane, cork, a phone book, anything like that is a form of damper.
Damping only works when the two parts are coupled together. Therefore, damping is a form of coupling. The difference is when the material being coupled is rigid and inflexible we call this coupling. When the material is soft and yielding we call it damping. Either way, coupling.
Decoupling, or isolation, allows the isolated component to vibrate freely on its own. Because if it touches anything the physics of mechanical vibration dictates this vibration will propagate into the adjacent material.
We all know if you hit a table, the water in the glass across the other side of the table will move. There is even a famous movie where the first hint of the T Rex is the water in the glass. The glass that is in the car. The car with shock absorbers. Dampers. Coupled to the ground, car, glass, water.
Even with all that earth, tires, dampers, dashboard, and glass in the way the footsteps of the dinosaur travel right on through to the water. Only slowly. The vibrations are slowed and smeared, but still there. We all know this, which is why Spielberg uses it.
Damping is a form of coupling. It is damping and coupling that slows and smears. It is isolation that alleviates this. QED.