Damages Types in Monster Hunter World (MHW) are the different damage categories of the game. Both Raw (Physical) and Elemental Damage dictate the damage any attack does directly, while Status Effects convey damage and debuffs indirectly.
In addition to the following Damage Types, there are also two Types that are commonly referred to as True Damage and Parts Damage.
True Damage is any Damage that is not modified by a Monster's Body Part Multipliers. Sources include Gunlance shells, Bowgun Sticky Ammo, and Bomb Items such as the Barrel Bomb.
Parts Damage is dealt whenever a breakable part of a Monster's body receives Damage, and contributes towards breaking that individual part. It is not represented by an onscreen number. Breaking a Monster's body parts raises their Body Part Multipliers against damage, saps the Monster's Stamina, and may limit the attacks that it can do. Parts Damage can be modified with the Partbreaker Skill.
See Weapon Mechanics for an overview of all the factors that go into damage calculation.
Attack Power, also known as "Raw" is the physical damage of a weapon. This is further subdivided into three types, against which Monster Body Parts have varying resistances.
Sword slashes, lance thrusts, etc: Can be used to cut the tails off certain monsters.
Shield bashes, hammer smashes, etc: Reduces Monster Stamina and stuns them if hit on the head.
Projectiles, Arrows, Bowgun: Special properties depending on the attack.
If a Weapon wields Elemental Damage, it will often appear as one of five types against which Monster Body Parts have varying resistances. Some Weapons wield more than one type.
Status Effect Damage
If a Weapon wields Status Effect Damage instead of Elemental Damage, its attacks have a 1 in 3 chance to cause buildup towards a special Ailment. In this way, Status Effect Damage does not directly add extra damage to a Weapon's attacks, but is still useful if played against a Monster's weaknesses.