Psychiatrists are medical doctors who have specialised in treating mental illness. They have a grounding in general medicine and are experts in the biological aspects of mental illness and the prescription of psychiatric medication. While some have training in psychotherapy, this is usually quite limited. Psychiatrists generally priorities biology in their explanations e.g., they might understand depression as a sign of a chemical imbalance that is correctable with medication.
Psychologists are experts in human behaviour and development. They are often highly trained in psychotherapy and do not prescribe medication. Psychotherapy is well researched and provides benefits beyond symptom reduction such as gaining emotional maturity and improving your relationships. A psychologist might approach a depression as a sign of an internal struggle, having missing developmental needs, a lack of fulfilling relationships etc.
Psychiatry and psychology are not mutually exclusive and some cases respond best when they are combined. This is particularly true when the two professionals work together as a team. I do advise people if I feel a psychiatrist would be benificial.