As far as I know, they're all subcategories of
Magic (DAMAGE_TYPE_MAGIC)
Universal (DAMAGE_TYPE_UNIVERSAL)
Normal (DAMAGE_TYPE_NORMAL)
Those 3 have certain properties --
Magic acts like spells. It's stopped by Magic Immune and ignores armor.
Normal acts like attacks. It's reduced by armor and stopped by ethereal
Universal ignores armor, any immunities, and such