I guess those children that can do magic very well at a young age would have a sorcerer level. That means Harry would have at least 1 level in sorcerer, 1 level in warlock (his connection to the dark lord) and the rest of his levels would be wizard.
Voldermort and Dumbledore might have a lot of sorcerer levels; Hermione might be a pure Wizard (Witch) because of how much she relies on head knowledge.