What is the difference between psychosis and schizophrenia and are they related?

I have been trying to read up on these mental disorders, however I am still confused. Psychosis involves hallucinations and hearing things. Schizophrenia also involves these symptoms, yet I have heard that a person can have psychosis while being schizophrenic. I want to know the differences between then and if they are related in any way.

Psychosis is a break from reality that can include hallucinations, delusions, etc. Psychosis is a "symptom" of schizophrenia. It is also a symptom of Bipolar and other mental illnesses.

Think of fever and flu. Flu(Schizophrenia) is the disease and fever (psychosis) is a symptom, yet it can also be a symptom of other disorders as well.

Psychosis is a type of symptom involving hallucinations and/or delusions.

Schizophrenia is a mental disorder that includes psychosis, abnormal flow of thought, flat affect (lack of normal display of emotions), social withdrawal. It may also include unusual physical movements (odd posturing, catatonia, etc.).

Someone could have some psychosis as part of depression, mania, PTSD, Psychotic Disorder Not Otherwise Specified, or psychosis caused by a physical illness, head injury or drugs, but not meet the full criteria for Schizophrenia.