[sph]

That is mostly correct: psychologist do not prescribe, psychiatrists do, as they are in fact medical doctors.

In my case psychologist made the suggestion I had ADHD after 2 years of therapy, so they knew me pretty well by that point. It all made sense to me, and I went to a psychiatrist to get diagnosed and medicated.

Had I gone to a psychiatrist directly, they probably would have prescribed an antidepressant without spending 2 years getting to know me.