There are 7 magic types, each with 3 spell levels. Magic descriptions
can be viewed in Sora's customize menu.

Fire : Unleashes a small burst of flame.
Fira : Unleashes a potent burst of flame.
Firaga: Unleashes an incredible burst of flame.

Blizzard: Unleashes a gust of frost.
Blizzara: Unleashes a gust of frost. Longer range than Blizzard.
Blizzaga: Unleashes a gust of frost. Longest range.

Thunder : Calls bolts of lightning to the target area.
Thundara: Calls a powerful lightning storm to the target area.
Thundaga: Calls a great maelstrom of lightning to the target area.

Cure : Restores a little HP to one character.
Cura : Restores a lot of HP to one character.
Curaga: Restores a massive amount of HP to one character.

Gravity: Wrings a percentage of HP from the target.
Gravira: Wrings a percentage of HP from the target. Wider area of effect than Gravity.
Graviga: Wrings a percentage of HP from the target. Wider area of effect than Gravira.

Stop : Prevents target from taking action for a limited time.
Stopra: Prevents target from taking action for a limited time. Wide area of effect.
Stopga: Prevents target from taking action for a limited time. Widest area of effect.

Aero : Deploys a barrier that absorbs damage.
Aerora: Deploys a barrier that absorbs damage. Damages enemies on contact.
Aeroga: Deploys a barrier that absorbs damage. Deflects certain attacks.

Locations:

To obtain new spells and upgrades, you must complete certain events.
These events are listed below according to magic type.

For each magic type: the 1st spell you obtain will always be the basic
spell. After clearing another event, your magic will be upgraded to
the 2nd level (-ra) spell. You receive the 3rd level (-ga) spell
upgrade after clearing all 3 events.