Wikipedia: "A delusion is a mistaken belief that is held with strong conviction even when presented with superior evidence to the contrary. As a pathology, it is distinct from a belief based on false or incomplete information, confabulation, dogma, illusion, or some other misleading effects of perception."

The point is, I think, that the delusional/conspiracy-minded believer goes on believing despite all evidence to the contrary. Like the guy who shot up the pizza place when there wasn't even a basement there.