Subtyping schizophrenia can be very tricky as there may be overlap in symptoms from one subtype to another. You could read about th DXM-V criteria for schizophrenia and see what they are, if you want to learn more about all this. Just google it.

I have bipolar type 1, but I spend a ton of time psychotic, so, have much in common with people with schz. It has just been my experience, knowing a bunch of people with these illnesses over the years, that some are very open with their delusions, want to convince others they are true, etc., and others are not. I suppose the paranoid schizophrenic may be more inclined to the latter, but the experts here can say more on that much more reliably than me.

Good luck to you and your dad. Very glad he is getting some help.