The confusion is common and has practical consequences: people reach the wrong professional and leave with the impression that “it didn't help”.
The psychiatrist completed medical school and specialised in psychiatry. They can diagnose, prescribe medication and issue medical documents. Some psychiatrists also do psychotherapy, if they trained separately, but many do not — their consultations are shorter and focused on symptoms and treatment.
The psychotherapist has completed several years of training in a specific method — cognitive behavioural, psychodynamic, systemic, gestalt — including personal therapy and supervision. They work through structured conversation over the medium or long term. They do not prescribe.
The clinical psychologist can carry out psychological assessment, testing and counselling. Without separate psychotherapy training, they do not do psychotherapy proper.
In practice: if symptoms are severe — you cannot function, you have not slept for weeks, thoughts of harming yourself appear — start with the psychiatrist. If you want to understand and change a pattern, see a psychotherapist. The two are not mutually exclusive: for moderate to severe depression, medication plus psychotherapy outperforms either alone.
One detail worth checking, whatever the title: the right to practise. A title alone does not tell you whether the person is accredited to work.