I think it has to do with both what use it is given and what background the user has
White magic is more used as "support" magic, be it healing, buffing, purifying and even reviving allies, while the spells that deal damage with it tend to deal at least some holy damage or heal either the caster or its allies by some of the damage inflicted. This magic is usally waved by characters with holy backgrounds or proffesions, like clerics, paladins and such, or characters related to the gods, specialy those affiliated with Lumia and her valkiries
Black magic, on the other hand, is mostly "attack" oriented, almost every spell out of it is thrown to damage, dampen or incapacitate your foes in one way or another. This magic also tends to deal blight or psychic damage, and almost every single offensive spell aplies one or more status effects on the target. This one is more used by your tipical witch or arcanist, characters that focuss on the study of magic and its aplications, always seeking knowledge, as well as characters involved with demon buiseness, like cultists or the imps themselves