With the understanding that these terms aren't defined in any way other than soft conventions of use, I'd probably say that equating high-fantasy with "scientific fantasy", for lack of a better term (magic is used to power devices and help improve the human condition) aren't the same, although they are commonly correlated.I think my opinion on what constitutes low fantasy is different to yours. I see D&D as high fantasy because you are expected to collect magic items as you advance levels, and you need magical healing and easily get it with a cleric.
Whereas WFRP doesn't give out magical weapons like candy (if at all) and magical healing is rare.
Disease in D&D is no threat with the aforementioned cleric whereas WFRP lists gruesome diseases that threaten the health of characters.
So to me WFRP is low fantasy despite having wizards who can blast the heavens. But as you say, it can also come down to the GM running it.
Depending on how magic is structured, you could easily have a low-magic but high convenience setting, where the only magic is potions and tinctures to cure disease and trauma, and small devices to help with daily chores (an enchanted cookpot that can warm itself, a magic icebox). It sort of reminds me of the items powered by sygaldry in the Kingkiller Chronicles.
Likewise, you could have a high-magic but low-convenience setting, where wizards can raise undead armies and blast apart cities, but no one has magic that can mend a sword blow. Like a setting where the only types of magic are pyromancy and necromancy.