Classical hypnosis was based heavily on hypnotic suggestions, where the hypnotist “convinces” the unconscious mind by direction and repetition to change the behavior to the one desired by the client. These suggestions could be something like this “You are a non-smoker,” “You do not crave cigarettes,” “You are happy about your decision to quit smoking.” Through time some hypnotists adopted techniques that were more “Therapeutic” in that they involve re-interpretation of past experiences and parts therapy. To distinguish between the two strategies for conducting hypnosis and to further separate stage hypnosis from clinical hypnosis, someone thought of the word hypnotherapy as something done by a hypnotherapist.
Not all hypnotists like this word, especially since a hypnotist is not an officially recognized therapist. To avoid sending those signals, some hypnotists only refer to themselves as hypnotists conducting hypnosis, even though others classify their methods as hypnotherapeutic techniques. This makes it challenging to separate classical hypnotists from modern hypnotists, who apply methods that are said to be more effective.
A good rule of thumb when you are looking for a hypnotist, a good rule of thumb is to check their certifications. A certification at NGH (National Guild of Hypnotists) ensures you that the hypnotists, as a minimum, have gone through the training required to achieve this certification. To continue the membership of NGH, the hypnotist must educate himself each year to keep his NGH approval. Other certifications ensure similar standards in the US, but be aware that some certification programs allow for home study of hypnosis!
Here’s an article on the difference between hypnosis and hypnotherapy for those who want to know more.