There are four kinds of Magic, and each has different strengths and weaknesses.

Fire.
Fire magic is what I like to call the basic magic, as it has more balanced stats than the other magics. Fire magic is a standard to put on all your Tome wielding characters.

Thunder.
Thunder magic is less accurate than the other magics but it hits hard, doing more damage. Thunder tomes also have a chance to crit unlike most other tomes.

Wind.
Wind magic does less damage than other magics, but it's very accurate. It's also very effective against air units such as wyvern and Pegasus riders.

Dark.
Dark magic is set apart from the other magic because only dark mages and sorcerers can use it, unless you have the shadow gift skill. Some Dark Tomes have varying side effects such as increased critical chance or hp draining. They are inaccurate like thunder spells.