Is hypnosis the same as being asleep?

No.

The hypnotic trance state is a “pre-sleep” state. If you fall asleep during hypnosis, or self-hypnosis, then the changes are unlikely to embed properly. This is one of the reasons that I always recommend sitting cross-legged on the floor for self-hypnosis; it’s much harder to fall asleep in this position than if you are sitting in a comfy chair.

(If I’m hypnotising somebody however, I always use a comfy chair!)