Anyone Out There From Japan?

This probably counts as an esoteric question even if you are Japanese, but here we go.

I’ve found two clearly related words for magic (well, more than two, but these are particularly related): mahō (魔法) and majutsu (魔術). Now, majutsu seems to translate to ‘sorcery’ rather than ‘magic.’ In English, that’s a matter of etymology. Sorcery derives from the Latin for fate. Magic stems from Ancient Greek (magus, a magician, so magic is what magicians do…). I’d like to know what the difference is in Japanese.

Now, both words seem to be related to demons. If I just take the separate ideograms, mahō is ‘demon law’ while majutsu is ‘demon art.’ Mahō seems to be the more commonly used word for magic, but I have a small sample size. If anyone can clarify this for me, that would be fantastic.