Witches and Magi do not exist as separate player options in D&D 5e. I’m not sure they should be separate. I have no idea what would set a magi apart from a wizard, and very few ideas that would set a witch apart from a wizard. Magi are probably best represented by Divination Wizards. Witches by Warlocks or Enchantment Wizards, or even a Druid.
This is why I’m against classes restricting which races can be them. There’s a lot that can be done through slight reflavoring.
I’m also feel that “no, those people can’t be wizards, they’re too barbaric and stupid to understand the enlightened magicks of our white European Merlin/Gandalf/Odin wizards, your mages are just untrained cheaters/orientalist knock-offs” is probably best to be rid of. It tends to be used in Eurocentric ways and echoes real world biases (I.e. the colonial urge to dismiss all aboriginal priests as merely “shamans,” for example). They can just be Wizards with whatever necessary reflavoring.