True, the hallucinations are more of bad train of thoughts that simply make you think something is there, when it really isn't.
Imagine saying "There's a purple elephant in the room" and you keep thinking it. You'll soon start believing it, internally reacting to it, talking to it, visualizing it and so forth. The purple elephant isn't ever there, but you've believed it so much that your rational mind simply does not care.
For schizophrenics, just get rid of the "Force your rationality" part out, and there you have schizophrenia.
However, there are many forms of schizophrenia (Which is essentially Thinking Seperately from Reality and Logic)
There is Paranoid Schizophrenia, where the delusions come from Paranoia and lead to paranoid tendencies. This is different than a Paranoia Personality Disorder, because there is a sincere belief of paranoia, and active steps are taken to prevent such things. The Steps/Beliefs are often Irrational/Delusional whereas someone with PPD may have legitimate reasons, or its not that much of an impact on their lives.
There is also Catatonic, and Disorganized, with two additionals called Uncategorized and Residual.
Essentially, Schizophrenia is a curious thing; to those who sincerely have the problem, it is a terrible thing. However, legitimate cases of schizophrenia are few and far between due to the "Quick to diagnose/perscribe" nature of modern psychology. There are many examples of "Over active imaginations, Overburdened Personality Facets, and even Active Neglect of Parents/Doctors (parents/doctors who just want their kids/paitents to shut up)"
Schizophrenia, while not everything what people imagine it to be, is still a psychosis of The Mind; and is essentially living life without Logic. It is the End of the Sidewalk, where the Void of Eternal Creativity lay. It is a land where Bohemians live in anchored tents artists parachute, eccentrics bungee jump, and where those without Logic are swallowed whole.