Indeed we tend to consider a “mentally ill” person as, let’s say a schizophrenic, (i.e. we define that person via his or her diagnosis). With physical diseases, we do it differently.
We don’t say, “Oh there’s a broken toe”. We say, “That’s John with a broken toe.”
That says a lot about how we perceive mental illness, and most particularly, those people affilicted with schizophrenia. Often the person gets lost by focusing on the label.