Each job is different in its function, including each pet job functions differently. The only thing needed to define a job as a pet job is the ability to have a pet without a subjob that brings a pet out for you. No matter what the pet is, you're allowed only one, whether it's a wyvern that acts based on what you do, automaton that acts based on what strings you pull, beast that acts based on what you tell it to do, or avatar/spirit that acts based on what blood pact you use.