I think the difference between these different types of practitioners is the degrees they have and what they are allowed to do as a result. A psychiatrist has gone to medical school, has an MD degree, and can prescribe meds, but they usually do relatively short visits and don't have time to do talk therapy. Therapists have either a master's degree or a PhD (usually in social work or psychology) and they can't prescribe medication but they do talk therapy. You can see both a psychiatrist AND a therapist if you want talk therapy AND meds--this is what I do. I see the therapist once a week and the psychiatrist every couple months for a med check.
I will second the Psychology Today website database to use for finding a therapist. I had a therapist I liked a lot who was retiring, and she recommended that to me as one resource for finding someone new. And usually once you find a therapist you like, they can recommend a psychiatrist if you want to discuss/try meds. I agree with the above poster who said that psychiatrists know more about getting meds right because they specialize in mental health, compared to GPs who have a medical degree and can prescribe psychiatric meds, but have to know a little of everything and don't specialize in mental health.