Nobody bothers observing what the difference between insanity and madness is.

Insane: a subjective observation you make about another, they clearly have a self-consistent reasoning process with a metric that you don’t share. But communication and cooperation is still possible. Aka Neurodivergent

Mad: an objective observation that someone is illogical, goes against established and observable evidence, may harm self or others, aka nut case

Edit: clarified sentences