Both psychiatrists and psychologists conduct psychotherapy and research, but there are significant differences between the two professions.
The first difference is in education: a psychiatrist has a degree in medicine, and is a medical doctor, whereas the psychologist has a degree (a masters or a doctorate) in psychology. The second difference is that a psychiatrist can prescribe medication, whereas a psychologist cannot.
If you are trying to choose between the two careers, you will need to determine if you would prefer to assess, diagnose, treat and prevent mental illness and be able to prescribe medications to your patients (psychiatrist), or if you would prefer to conduct psychotherapy, administer psychological tests, and conduct research (a psychologist).
A neurologist is a medical doctor who specializes in treating diseases that affect the human nervous system.