All three titles mean someone is committed to helping you with your mental health via talk therapies. Here in the UK (other countries differ) the difference is one of education and training.
In general, a counsellor has done three or more years of training with a largely practical, hands-on approach and some theory.
A psychotherapist might be a counsellor who then continued on to complete a psychotherapy MA. Or it will be someone who went directly to a school of psychotherapy for all of their training, which is a hands-on but also theory-heavy route, and concludes at the MA level (4 years in total, often more).
A counselling psychologist took a different route entirely, finishing a BA in psychology then going on to do a conversion MA in counselling psychology, where they learned how to apply what they have learned to working one-on-one with clients. It’s a less hands-on, more scientific entry into working as a talk therapist.
Want to learn more? Try reading the following articles: