The main muscle associated with teeth-clenching is the Masseter (jaw muscle). Botox is administered into this muscle to relax it so that the bite/clench will not be as strong.
This helps to alleviate the symptoms/discomfort of teeth clenching such as headaches, widened jaw, teeth damage, facial pain and pain in the jaw joint (Temporomandibular Joint).
Once treated, results can last up to 6 - 8 months before the procedure is repeated again.
I will personally recommend administering the injection to a relaxed jaw since it will be less painful and uncomfortable for the patient. Otherwise, there is no difference in the effects, whether the jaw is clenched or relaxed during treatment.