There are many different ways to group characters, some of which such as "Race","Element" and "Weapons" are conditions that powerful weapons require for the effect to take place. Bahamut, Revenent, Seraphic weapons are such examples. They are essential to your grid and provide an enormous damage boost. The following list shows the categories and their types.
Rarity: SSR, SR, R
Element: Fire, Water, Earth, Wind, Light, Dark
Style: Attack, Balanced, Defense, Heal, Special
Weapon: Axe, Bow, Dagger, Gun, Harp, Katana, Melee, Saber, Staff, Spear
Race: Draph, Erune, Harvin, Human, Primal, Unknown
Sex: Male, Female, Other