[Authority] is the dominance over a creature. It is a symbol of absolute loyalty. The holder of the [Authority] has all access to the creature's ability and power, they also have all rights to do whatever they want with the creature and the creature can't go against it. 

A [Contract] is a temporary and inferior version of [Authority].  The contractor can use the creature's ability but not to the fullest, they can telepath and summon any time. 

The [Gods] were the original owner of [Authorities]. They created the [Authority system] so they can rule over all creatures. After they sacrificed themselves to sealed Eve, the [Authorities] they had were released and the creatures can now choose their own master.