As someone who has a BA in psychology, I'm gonna tell you the difference, this going to be quite a long answer.
A psychiatrist, a psychologist and a therapist are different in the way they handle patients and their education background.
A psychiatrist is usually a doctor, they have to take a medicine degree, and then continue their education as a psychiatrist, this, given the medicine background, give them the ability to give patients medications. Also, usually, a psychiatrist treat patients that have more severe mental illness, who often need medication to help their treatment, this patients usually belong to the psychotic category, such as bipolar disorder, schizophrenia, etc.
A psychologist, is someone who has a psychology background in their education. Psychologist is usually more focused in using variety of techniques to treat or help patients. They can't and don't use medication to treat patients. A psychologist, given their educational background in assessing and analyzing human behavior, have the ability to diagnose people with mental problems. So, they can give patient a diagnosis as well as treating or helping them to recover. A psychologist also usually treat patients with less severe mental problems, like depression, career or relationship problems, mild anxiety problems. That's why we have school psychologist but no school psychiatrist.
A therapist is someone that help patients resolving or recover through their problems, they work with patients, but are not necessarily expected to diagnose patients. Usually a therapist can come from any educational background as long as they have been trained or are experienced in working with people with mental problems. Therapist usually doesn't work alone, they will always have a supervisor (can be a psychologist or a psychiatrist) that they have to report the patients progress to. They are the executors of the treatment and are there to help psychologist and psychiatrist.