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.
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.