The school your proficient in is just the overall category, the 'type' is more specific. For example, you're proficient in 'control' magic but the type is 'Fire'.

After re-reading the OP it does seem a bit unclear, I'll go over and edit out The words 'type of' and just leave 'Magic'. Also I'll change proficiencies to school of magic. There's some typos in there that I missed as well so I'll edit those too. [@KatherinWinter]

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Its been edited.