Spells: Magic, these can deal damage from close or afar, or heal, or inflict status effects. Spells are the main arsenal of a pupil-based class, and if you're using one - you're allowed to make a new spell every level.
Skills: Used by Melee and occasionally Ranged classes, a skill is not considered a spell yet it still uses your character's mana. Skills are special/fancy attacks that your character does to deal more damage than normal.