The following are the types of damage.
Slash: This follows Axes and other blades. It causes cuts ect.
Bludgeoning: Caused by fists, Hammers, Special tipped Arrows, clubs and staves and other blunt weapons.
Piercing: Stabs, Arrows, and anything else that will penetrate skin. Normally causes lethal damage.
Force: Like the recoil of a Grenade force damage is a burst of air or otherwise. This can cause push back, disorientation but is hardly ever lethal.
Electric: Shocking damage that attacks the nervous system and possible burn skin. Mid level damage causes stun. High level damage cause permanent psyche damage.
Burn: Burns are caused by fire damage. Can cause permanent psyche damage and can be lethal.
Smoke: Smoke can't cause damage unless it's heavily concentrated even then it's low damage mainly focused on 1 LP and 3 Temporary PP.
Psyche Damage: This is damage to the mind (PP) and can come from nearly anything. Some spells can attack this directly but it mostly comes from disturbing actions or situations.
Poison: Poison is a slow burn on any of the three health gauges. Untreated it can cause more damage then a stab wound and vary in ways to heal.
Life Force: Very Rare but very powerful. Life force damage is a direct attack focused on LP rather then HP and is magic/alchemy forbidden by law. Making it, not just it's practice extremely rare.