That sounds like a good way of understanding it to me. Metals corrode, wood roots, plants and animals decay. But some things like builings can rot and decay. Rot can refer to any organic material. We also use all three words to refer to a decline in quality of immaterial things like values, morals or thinking.

I think which one we would use would depend on the speed of the action. Rot: quick Food Decay: slower Teeth, Cities Corrode: much slower Metal, Infrastructure Corrode also feels very "clinical". "Rot" feels common and unpleasant. "Decay" is somewhere in-between.