Let's say Bob is seeing things. Hearing things. He might in fact be completely and totally disconnected from what's actually going on around him, hearing voices in his head, and all of that stuff.
And yet, in reference to his percieved reality, Bob is perfectly sane, stable and rational. The voice in his head tells him to kill his wife, he tells it to shut up and remember just who owns this mental space. He's not paranoid, rash, violent, or panicky.
Bob is, in other words, Sane On The Inside: A perfectly functional and sane person wrapped in a shell of mental delusions.
There are two main types of this:
TYPE 1: The person is insane, but catches on to this fact and actively attempts to fight against it by attempting to distinguish what's real from what isn't.
TYPE 2: The person is insane and does NOT realize it. However, while all of the information he's getting is completely incorrect, what he does with this incorrect information is perfectly reasonable. If you were actually in the situation this person thinks he's in, you'd be doing a lot of the same things.
This trope is extremely common whenever the main character is at all insane, especially in video games.
- In Penumbra, when Philip's infected with the virus, he starts hearing voices from an entity named Clarence. Clarence actively messes with his head, making him hallucinate and the like, but Philip himself is still completely and totally sane.
- In the second Bioshock game there's a scene where you play as a Little Sister which reveals they see everything through a filter that makes the city of Rapture appear as a Crapsaccharine World and presumably still think like a perfectly normal child would.