The magic are divided in five categories. Here are some information about them.
Black Magic
Black magic specializes in Offensive spells only.
It includes Elementery Techniques, Curses and Additional Damage spells.
Ex: Fire, Blizzard, Bio, Ultima etc.
White magic
White magic are known for its holy Medical and Synergistic spells.
But in White magic has some offensive spells like Holy
Ex: Cure, Protect, Shell, Esuna.
Summon Magic
Summon magic is a special type of magic that only L'cies can use.
It allows the caster to Summon an Eidolon to fight for them.
Ex: Summon Shiva, Summon Ifrit, Summon Bahamut etc.
Weapon Magic
Weapons are mostly used for non-magical reasons.
But there are some Weapon magics to combine with.
Ex: Enfire, Enthunder, Flamestrike, Sparkstrike.
Limit Magic
Limit Magic, also known as Limit Breaks is magic who is used by Everybody.
It's not like a forbidden L'cie magic really, it's more like a abillity that runs through your blood.
Limit magic is basicly a '' super attack '' that takes lot of the users Energy to do.
Ex: Braver, Heavens Wrath, Pyroclasm, Slice and dice etc.