There are 4 types of rewards for killing monsters: Ownership Reward, Rally Call Reward, Rally Participation Reward, and Support Item.

Support Item: Used by the Captain to help others in attacking event monsters

Ownership Reward: Owners will only obtain this reward regardless of whether the player initiates or participates in the rally

Rally Call Reward: Non-owners will obtain this reward after helping others (the Captain) in initiating a rally

Rally Participation Reward: Non-owners will obtain this reward after helping others by participating in a help rally or a rally initiated by the owner