Is schizophrenia related to depression?

Not really: It is possible to have major depression with psychotic symptoms and it is also possible to have schizophrenia and to become depressed. In general, schizophrenia is considered a thought disorder and depression a mood disorder.

In the real world: Lots of symptoms overlap between schizophrenia and depression, especially manic-depression. Many patients with schizophrenia also have depressive symptoms. Furthermore, some patients with depression also have hallucinations, delusions. Several antipsychotic drugs are effective as treatment of schizophrenia, manic-depression, and depression. There are also overlaps in genetics.