Adept is only the ability of the spell, any spell. To find the class, go to a spell list and just look for the name of the spell.
Smite Apprentice 1 and Smite Adept 1 will still be Smite, just better.
Sometimes the text of the spell will mention the class it's for, but not always. You can also Google it to get enough leads on where to go.
This is a good site for spell lists.