Big Book O' oc Lore

Physical - physical damage is exactly what it sounds like, I don't think there's really much of a need for me to elaborate here. Physical damage is sometimes also referred to as red damage

Special - special damage is like a sort of magic damage. Like physical it's a direct attack to the body but it's strengths and resistances are based on special attack and defense rather then physical ones. Special damage also tends to better effect those without any physical form, like ghosts for example. Special damage can also be referred to as blue damage 

Mental - instead of an attack to the body mental damage is a psychological attack directed towards the mind. Despite what it may sound like mental damage and psychological trauma aren't inheritably one in the same. Mental attacks drain HP like most others. It's dependent on the ability(s) used that effects if these attacks deal lasting trauma or not, much like all other damage types. Can sometimes be referred to as white damage

some attacks are able to deal multiple types of damage at once, these combinations usually get their own name's to more easily categorize them

Violet Damage - a mix of physical and special 

Pink Damage - when physical and Mental damage mix, it's considered the most uncommon type aside from black damage

Cyan Damage - fusion of special and mental 

Black Damage - considered to be the most dangerous, black damage occurs when all damage types mix together