Once you get a certain amount of special attacks, they are all categorized in 3 categories:
Offensive, Defensive, and Special.
Offensive is basically your Black Magic spells, like Fire Claw, Fiery Explosion, Spore Spray, etc.
Defensive is your list of healing and buff, as well as summoning, spells, such as Healing Spray and Fury.
Special, however, is a made up category that lets you use the spells that certain monsters use that cannot be learned from cards, you actually have to be hit by one for a chance to be able to learn the magic. (Similar to Blue Magic from the Final Fantasy series.) It has a 1/10 chance to be able to learn the attack that the enemy used at you. An example of a (hopefully at some point) up-coming attack is Dimensional Tear (From the antagonist of the game's 2nd encounter.)
Edit: There might be some special accessories that boost the chance of letting you obtain a Special Magic Attack, such as the Philosopher's Book, a relic that increases the chance of learning the attack to 1/5, and can be stacked with other Philosopher gear.