Both involve being very relaxed it's true.
However, self-hypnosis is about relaxing and using very basic techniques like, positive mental attitude or positive suggestion to help you accomplish the things you desire. And by the way although I say these are very basic tecniques, they are also very easy to get wrong if you are untrained. It can also include listening to pre-recorded tapes that are not personalised to you - just to the things you are aiming for. You can even buy a book of scripts and record your own to listen to and your own voice is often more effective that a strangers voice.
Whereas with hypnotherapy it is the last bit of the word that has the impact - therapy. So when you are with your therapist they should firstly take some time to talk to you. Depending on your therapists training and experience the therapy could be based on a number of techniques and these should be personalised to your needs.
The other important advantage of therapy is that the therapist can see beyond your understanding of the problem and that is often where the solution lies. A good example to illustrate this is dreaming. When you have a dream you sometimes have an idea about where it came from but often (especially with the weird and wonderful ones) you have no idea why you should have dreamt that. Your therapist, when presented with your dream, will be able to relate the dream to what s/he knows about you and often will be able to find a meaning that escaped you but that makes complete sense to you once you have heard it.
However, hypnosis and hypnotherapy are never more than a deep relaxation and you can experience the same in many situations. You are not asleep but not fully awake and in that state similar to when you are daydreaming or drifting. It is also not unusual, if you are using a tape, to feel as though you stopped listening at the same place each time after you have listened for a few times. You have not gone to sleep but just gone somewhat deeper and it is perfectly normal.
Senior Hypnotherapist and Trainer.