I suspect the talk therapy may be a short part of their training and not their main focus? A psychologist will train for 7 years (two years prac) with all the focus on the talk side of things. A psychiatrist trains as a medical doctor and specializes in mental disorder. You were probably lucky to find someone who placed a lot of emphasis on the talk therapy side.
My AS went to a psychiatrist whilst in the throes of addiction. In his first session he was diagnosed as bipolar and prescribed some strong medicine with fairly harsh side effects. His follow-up sessions consisted of a 10 minute visit to find out how the medicine works. No therapy as such.
As I said, my youngest son would have seen the psychiatrist for anti-depressant prescriptions and continued with his talk therapy with the psychologist.
I know a lot of people refer to psychologists as psychiatrists in error (not saying it is the case with you).
Where I have a say, I would always go for a psychologist first.