Timing. Major depression with psychosis means that the person has no psychotic symptoms when they are not depressed. On the other hand, schizoaffective disorder means the presence of even subtle psychosis between episodes of depression or mania.
Depends on symptoms. A person who develops a depression with psychotic features will experience hallucinations and delusions only when they are very depressed. A person who has schizoaffective disorder will continue to have hallucinations and delusions after his/her mood improves and those symptoms can last for weeks or months afterwards.
Psychosis timing. For those with major depression with psychosis, the key is that the psychotic symptoms never persist after the depression goes away. Schizoaffective disorder results in psychotic symptoms occurring without and independent of depressive symptoms as well as with them.