Oh my daughter's tantrums were pretty demonic. A friend of mine who is a nurse saw one and said I should have her evaluated for epilepsy because it almost looked like a seizure to her.

The intensity of the tantrum is a difference to us, but to the child a tantrum is a tantrum. They aren't any more or less in control of a bad tantrum than a mild one, so reacting differently to them based on intensity is only for our benefit - there isn't any teaching value in that. And "discipline" means teaching, not punishment, so it's important to keep in mind what is being taught.