Difference Between Health Regeneration and Healing?

I was testing out revitalize on Singed, thinking since he uses corrupting potion and his ultimate gives health regeneration, that surely this should be a great rune to pick up. However, the bonus healing counter did not increase for either the potion or the bonus health regeneration. So does bonus health regen/health regen not count towards this rune at all? Would it count for Mundo? According to the league wiki, Mundo's passive and ultimate give him percent health regen. Would this still not count as healing? I am so confused now.

Also Iron Skin and Mirror Shell don't proc from bonus health regen, and those are supposed to be proced by healing.

Can someone please help me define what goes under "healing" lifesteal? spellvamp? or just things from supports?