So I was just wondering if the perks in the different schools of magic are spells, or just damage boosters/add ins and you have to buy the spells separately.

They're separate, but some perks "upgrade" your spells. For example, one perk allows you to charge up your spells assuming you have the same one in each hand.

Perks act as damage boosters, and other benefits. The spells you have to learn from books or buy from a store.