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If a witch is someone who practices witchcraft while a wizard gains magic by studying (rather than being magic genders), then a witch can also be a wizard if they studied and/or went to school for it.
Which is why I postulate that Hogwarts School of Witchcraft and Wizardry was created specifically to allow witches to gain the benefits of wizardry through standardized schooling rather than having to study it themselves with less resources, safety precautions, and experienced teachers.
It was only later on in time, when separate schools for male and female were common among non-magicals and combined schools were specified, that someone or other assumed the name meant the school was for both genders (as both attended) and accidentally started a fad of referring to female witches as witches and male witches as wizards as the other students found their misconception amusing.
This became a commonplace habit, and eventually pervaded the entirety of British witch/wizard culture to the point we see it at in Harry Potter.