A Psychiatrist is a Psychologist which can prescribe medication. I don't know how it works in U.S. but here they just ask you at the start of the session what your thoughts are on medication and they tend to be more happy if you refuse it. It's more sessions for them anyway in the long run.
If you are in the U.S., Psychiatrists will often ask who your therapist is. If you are in the U.S. keep in mind that they may be expecting you to work through traditional therapy while they work on your drug regimen. They certainly know how to offer non-drug therapy but many have become medicine coaches due to the way the system works / patient expectations work.
At least here in the US, psychiatry is a specialization of medicine, and a psychiatrist is an MD, while psychology isn't a specialization of anything, and its practitioners' credentials vary widely. The disciplines don't really have much inherent overlap; nobody goes to a psychologist for a prescription, which they can't provide anyway, and nobody really goes to a psychiatrist for "talk therapy", which they mostly prefer to leave to the psychologists whose primary realm it is.
