You go to them both because you're having trouble casting spells and a wizard is listening to u speak and thinking "oh thats just Godzboggle's fourth rhyme incantation probably. whens my dinner i am so fucking hungry right now" whereas a witch is listening to you speak and thinking "theres stress in that face and voice. also theyre continually dehydrated so of course their hands cant grasp the wand right. ill pencil them in for a tea at noon and maybe theyll drink more"