Your question is one that many ask and I can see why it would be easy to not clearly know who is who and what is what given the plethora of healthcare staff. Becoming educated about what the credentials and scope of each person involved in your is a step in becoming a true partner in your care. The more you know, the more empowered you are as a patient.
Here is the difference between the two:
1. Psychiatrists such as myself are physicians, meaning they are "Medical Doctors" as defined as either having an MD (Doctor of Medicine) or a DO (Doctor of Osteopathic Medicine--same as MD, just additional curriculum). We are licensed by the Medical Board of California and complete a four year medical residency, then take a two part exam to become diplomates or "specialty board certified" by the American Board of Psychiatry & Neurology. We practice medicine and are licensed as such. Our first year typically is in general medicine, pediatrics and neurology. We also learn the six main therapeutic modalities--i.e. CBT. But this is only part of our education. Our foundtion is in medicine and we use that knowledge along with our psychotherapeutic training to diagnose and treat patients across all psychiatric disorder spectrums.
Psychologists while referred to as "Doctor", are not physicians. They had either a PsyD or PhD in psychology, which is based on studying behavior and the therapeutic modalities also learned by psychiatrists. Psychologists spend more time learning talk therapy. They do a one year "internship" which is seeing patients while supervised by a licensed psychologists. There is no speciality board for psychology as it is not a medical specialty. They are licensed by the Psychology board.
From my experience, and what evidence shows is that treatment in talk therapy is more effective if the patient is also being treated with pharmacological interventions as there is no way to separate the neuroscience of the brain from the rest of medicine. Your brain is attached to the rest of you which is governed by multiple complex processes, genetic variabilities, etc.
The right medication can help patients reach a point where they are more open, forward-thinking and thus able to make better use of their time in therapy.
I hope that helps.