Familiars, more commonly called Companions (even Pets by some), are a strange phenomenon. They take on many shapes and forms, but only very, very rarely appear as anything resembling a dinosaur-like species. Their appearance is determined by the theme/focus of the individual they are bonded to. They cannot be bonded to humans.
When called Pets, this is often in reference to those bonded to Whifflings instead, as then they may take on a weak magical ability. When bonded to Paralogos, this phenomenon does not occur.