To me, therapist is the overall word for anything talk therapy related. So psychologist, psychiatrist (if they do talk therapy and not just meds, and these 500 different credentials one can get otherwise.

To me, counselors were the only ones that couldn't effectively help me, since they are there more to guide you than to actually fix difficult mental health problems.

With my T, a psychiatrist, I never had that issue. But I'm pretty sure that some counselors would be able to help me, and some psychiatrists would not. Although you say that it's not an issue of finding the right one, it still is. For some people 90% of therapists might be useful, for some only 20% or less. Each therapist has a different way of talking, some might click well with you, some may not.