The overlap is not huge at all. Beside psychosis, they have no overlap, and the quality of the psychosis in the two illnesses is far removed from each other.
I also know of numerous people who have spoken publicly about receiving a schizophrenia diagnosis and having it later be revised to schizoaffective disorder.
I also came to the impression that it is common to receive a bipolar I diagnosis during a psychotic episode and have it later the diagnosed as schizophrenia or schizoaffective disorder.
Sometimes if your doctor sucks you may stay in the less accurate diagnosis, sometimes for years.