No, hypnosis is not the same as sleep, even though it may look like someone is asleep when they are in a deep level of hypnosis. During hypnosis we may have slowed breathing and muscle relaxation, and many clients even report after a hypnosis session that they can think clearer and they feel more relaxed or calm.
Sometimes a hypnotherapist may use the word sleep, but “sleep” just means go deeply relaxed quickly. It’s actually really important that you don’t go to sleep, as you need to be alert and attentive so you can follow instructions; your hypnotherapist will gently guide you into a heightened state of awareness and focus.