Pets (also called Animal Companions) is an NPC seperate from player characters which fight alongside them. Players can use skills specific to pets to augment their abilities. Squig Herders will have multiple types of summoned Squigs, that are disposable. White Lions will also have a pet that they will have throughout the entirety of the game, and will be quite customizable.
A Magus's disk, despite being directly controlled or influenced by the magi, is not considered as a "pet" in the strictest of terms.