Possession is a more specific type of ownership. An entity (the possessor) possess another entity when the possessor has the entity in its inventory. Possession is a persistant action that does not require triggering. Instead, entities begin to possess other entities as soon as they collect them, and continue possessing them until they are released. Possession implies ownership over the possessed entity.
In Diablo, player-controlled entities possess many items at a given time. Often, they must possess special items related to a quest in order to complete their quest.
Super Mario World
In Super Mario World, there is a character called Yoshi which Mario can ride. When mounted, Mario is in possession of Yoshi, with controlling Mario becoming the equivalent of moving Yoshi. When riding Yoshi, Mario is granted extra abilities.
Lord of the Rings: Battle for Middle-Earth 2
In Lord of the Rings: Battle for Middle-Earth 2, players can find and possess the One Ring; if a unit carrying the ring returns to the Fortress, it will allow them to summon either Sauron or Galadriel.