Behold the Wikipedia answer: "Cogsci is the study of the mind" and "Psychology is the study of the mind".
OK.
Psychology studies "emergent" properties of the mind: feelings, beliefs etc, and how these influence behavior.
Cogsci as a field seems to take a more reductionistic approach to roughly the same topic. It's broad in scope and takes input from psychology as well as linguistics, neuroscience, philosophy, computer science, AI, and anthropology. But I think psychology also takes input from linguistics, neuroscience, philosophy and anthropology?
However. A Freudian-style hypothesis like "You seek men that remind you of your father because you didn't feel fulfilled in childhood, blah blah…" slots into the field of psychology, and not much into cogsci. Cogsci does not tend to go down to such an object level on how feelings and beliefs interact, not while treating them as indivisible things.
Psychology is related to psychotherapy (therapy-based help) and somewhat to psychiatry (drug-based help). Psychology is an academic discussion that identifies and describes problems people have, and speculates about the possible causes, and then psychotherapy and psychiatry are the fields that develop toolkits for fixing these.
Whereas cognitive science … ? Screw it, I still can't pin down the difference.
Maybe their histories shed some light on it. Psychology started with Freud AFAIK, while I have the impression that cogsci started with Kahneman & Tversky's research into heuristics & biases, and is more interested in "small" hypotheses that involve equations, such as Piers Steel's Procrastination Equation.