So there is delusional disorder...

Delusional Disorder Symptoms | Psych Central

You can pretty much have any kind delusions but if you have the typical auditory hallucinations it meets the criteria for schizophrenia if it lasts long enough. If its shorter then schizophreniform. Materly, I agree with you in that my delusions were tied into my hallucinations which is one of the things that made them bizarre but some people believe perfectly plausible things that aren't actually true without ever hallucinating. The two processes seem to be independent in the way that you can have a cough or a runny nose independently but sometimes a single issue can cause both. The thing is there is not great research on delusions out there that I'm aware of, they are pain to treat and to me the absolute worst part of psychosis. I know when I started to relapse a little bit maybe a year and a half ago I had hallcuinations and delusions in a sporadic and unconnected manner. At one point I thought for example that my pdoc was working with the devil to suppress my powers with medication----I wasn't hearing voices or having any sort of hallucination when I though that. I was to the point of tears believing I had been tricked. In this case the whole thing was triggered by a mouse trap catching a mouse irl. The sound woke me in the middle of the night and my bird also started flapping about but I had no conscious awareness of the sound so for 3 hours I thought I was psychically connected to my bird etc.---it wasn't until morning when I saw the mouse that I put it all together and realized I was wrong. Now pdoc doesn't think it was a delusion because it went away with proof to the contrary but whatever it was you could have had pdoc sign on his own life that he wasn't working with the devil but I never would have believed it until I saw the mouse. All this was while on meds so I'm not sure what impact that had on the level of belief.