It's not exactly science anyomore, or maybe ne'er was. It is political diagnosis.
I don't know how the DSM treats those subjects. I know that it is a MEDICAL book. Written by doctors for doctors.
Psychiatrist = type of doctor
psychologist = type of philosopher, mystic, wordmonger.
A doctor is a kind of scientist. A psychologist is a kind of sophist(usually).
Psychologists are certainly constantly espousing such nonsense as what you have described. People's ignorance of the difference is useful to psychologists. They sell books and grow cults by seeming like scientists of the mind. They are no more scientists than English, Art, or Women's Studies professors.
A psychiatrist, the doctor, can write you a prescription if you have a chemical problem, or an emotional problem that can benifit from short-term medication. He can also do everything a psychologist does.
Psychiatry is a medical specialty, they get an M.D. after their name. Psychologists get a Ph.D.(if they finish their dissertation).
Like most doctors, psychiatrists have to do a 6 month internship in a field other than the one they plan to enter. Thus you might have psychiatrist who spent 6 months delivering babies before he ultimately got licenced to practice.
If I had a problem I would want to go to a psychiatrist rather than a psychologist.
But the DSM could have become corrupted by PC inanity recently, it wouldn't surprise me since it seems everything else has.