Now, enemies are completely different from characters when it comes to types. There types are more like elements, sort of like in "Pokemon." The Elements you have are wind, water, earth, grass, fire, ice, and normal. Mages are strong against the normal types and are average against the others. For the rest, however, the other Types are strong against them, depending if you are using special element weapons. For example, when you have a water sword, you can deal a great amount of damage to a fire type enemy.
Area bosses usually are normal types, because normal types aren't usually weak against any other elements. For the other enemies around different areas, you would normally see them with different element types.
That is how the enemies work.