Really they all seem to have had roughly common roots and then engaged in speciation over time by culture. "Witch" essentially meaning poisioner or "bad pharmacology/herbalism" ans posioned and cursed as essentially synonymous. Given that dose and application make the poison this ends up being a very dangerous look for any herbalist even before any cynical power grabs because they would always look guilty of carrying poison even if the foxglove was to steady the heartbeat instead of stopping it.

The split from Philosopher to Natural Philosopher which later split to Scientest and Philosophy of Science essentially are a more "modern" version of the same process.