I have pondered what the difference between these two words is for many years. I only just discovered the answer
A psychologist has a PhD in psychology. Easy enough to explain.
A psychiatrist is a medical doctor who had a three year residency studying psychology.
Neither of these is to be confused with a psychoanalyst, who is a psychiatrist or psychologist who has extra or specialized training in research and psychological theory.
May the light of knowledge shine on you all. There is no need to suffer in the darkness of ignorance when I have my A.P. Psych homework to do.