Not all the spells you see are a specific spell card, some are created using "Mutate" Treasure Cards.
Some spells are only available through quests for your school. You will only be asked to do quests for your main school, so spells that are learned through other school's quests will not be available to you.
Depending on your main school, you will have access to higher level spells as you progress. (since you're in Moo Shu, you have many already!)