I think it's important to explain what each role does.
Counselling psychology is based on the idea that answers are within you. The counsellor's role is to invite you to talk about your feelings, and thus unlock where issues may lie. In this way, you both can work out the best way forward.
Psychiatrists are more interested in the diagnosis, prevention and management of mental health issues. Based on their previous experiences with patients and theories, they will discuss and inform you of the best way to deal with your mental health issues.
Overall, the main difference is where the answers to your issues and problems come from. Counselling believes it lies within you, psychiatrists believe it is based on "universal" knowledge.
Much love <3