A delusionally paranoid person would make a claim: "There are dozens of people following me with the goal to ruin my life". Their perception isn't possible to reconcile with the objective reality of "No one is following you, and no one just whispered 'Now you see how it works' into your ear."
In the first case, the person isn't delusional about objective facts, but their subjective interpretation is unusual. In the second case, the person and an outside observer would disagree about things that you'd expect to be objective facts. If the first person told you "No, that's not a penis", then the two people would be equally unreasonable.
The difference is that it's difficult to apply objective reason to subjective experience.