I am mentioning my credentials because I have been complaining about people not distinguishing between psychologists and psychiatrists for many, many years. I am a little triggered by such comparisons.
The human psyche (incidentally not a word you ever hear in psychology (and potentially psychiatry) classes) is large, and psychologist and psychiatrists focus on very different things.
Like it's fine if you don't see a difference between the two subjects, but others do as they are very, very different.
I guess the closest analogy would be if I called you (a mathematician by training, i assume) a statistician.
Many people might not see the difference between the two roles, but I am relatively confident that you would.