In this regards,
this week, I held freezing metal for too long and have spots on my fingers that are pained and reddened. This frostbite is no different from a sunburn and will heal in a few days. Or this 'damage' and feeling is the same as if I were to get a mild sunburn from sitting outside.
There is no physiological difference between this and getting a sunburn, as it is minor and the body will fix it.
Acid/base damage is the same. If it is minor, then the body will recover easily from it. I've occasionally had small drops of concentrated acid/base on myself, once its been washed away, its fine with no lingering effects.
However, often the acid/base damage from malicious individuals is fairly intense, eyes will get exposed, and other body parts will be soaked for extended times. These are a bit scarier as the chemicals have time to penetrate the skin and do damage. Its these that cause the 2nd/3rd degree burns and are the disfiguring 'burns' that you're thinking of.