As we have discussed in other posts, a psychologist is generally concerned with the mind and behavior. Some services offered by psychologists include psychological testing, mental health counseling, talk therapy (such as cognitive behavioral therapy), and in some states, prescribe medications. As of this writing, those states are Idaho, Iowa, Illinois, Louisiana, and New Mexico.
A psychiatrist is a medical doctor (M.D.) or doctor of osteopathic medicine (D.O.). Some psychiatrists may offer counseling or therapy, but they also have a broader scope of practice than the psychologist. The psychiatrist can conduct physical exams, order lab work, and prescribe medications in any state. They also diagnose illnesses and manage treatment and provide a wide range of solutions for serious mental issues such as major depressive disorder, bipolar disorder, borderline, and schizophrenia.
Speaking of treatments, psychiatrists can provide a wide variety depending on the problem and what works best. Treatments can include medications, psychological therapies, and brain therapy (electroconvulsive therapy, for example). As noted above, psychologists generally see people who would benefit from psychological interventions for behavioral issues, learning issues, depression, and anxiety.
Of course, both understand how the brain works and how emotions, thoughts, and feelings influence our behaviors and health. Both can treat patients with talk therapies. However, since psychiatrists attend medical school and become medical doctors before specializing in psychiatry, they arguably have a more detailed knowledge of how mental illness and physical ailments are connected.
Psychologists and psychiatrists often work hand in hand. This could be in hospitals or as a part of a mental health team.