Payload refers to the flavor of pain that a particular projectile inflicts upon the unlucky recipient. Propulsion is the means by which a projectile propels itself from one place to another. Projectiles with propulsion types that have high thrust values cannot turn very quickly, and so they will perform poorly at homing onto a target. But such projectiles do have the benefit of being very speedy. Note that mines cannot have any propulsion.
Trigger is the means by which a projectile decides when to detonate.
All projectiles explode when they receive damage, such as upon impact, but a trigger allows a projectile to go boom for other reasons, too.