As an aside (it isn't really relevant to the conversation, just personally interesting to me) there is a pretty big difference between psychologists and psychiatrists these days, although 100 years ago there wasn't. Psychiatry is the branch of medical treatment that deals with mental illness; psychiatrists are MDs. There are MDs who do research rather than clinical work but that typically requires research training, thus there are joint MD/PhD programs. Psychologists are research oriented, and although things are changing all the time the breakdown tends to be that psychiatrists treat people, while psychologists study people. A medical doctor who specializes in the brain is a neurologist, while a research doctor who studies the brain is a neuroscientist. There is overlap, though.
Confusing matters, there are also clinical psychologists who treat patients. And, all PhD psychologists are trained and qualified to assess a person's mental state, although not all are trained and qualified to diagnose and treat illness.
Confusing matters even more, neuroscientists are not so much psychologists as molecular biologists or biochemists. There is also the emerging field of neuropsychology, but right now so few schools are offering that as a degree that most budding neuropsychologists kind of have to take a "build-your-own" approach.