Typically the term bonded refers to an animal who shows a preference for a particular caretaker. Some animals such as parrots will typically bond to another person accepting them and getting care from them and will often shun everyone else biting and becoming aggressive or defensive when being handled. My mom's parrot is a good example of this. He does not like when my mom and dad sit together and if he is left out he will attack my dad because he has developed a dislike for him because he takes time away from him. This can also happen if my mom handles another animal because he is extremely bonded. He does let me handle him although not in the same way. For example I can pet him and manipulate his wings but he'll usually bite if I try to pick him up. He'll let my brother pick him up but doesn't like him to pet him. For my mom he'll flip on his back if she wants him to but not me. Too bad he won't allow any of us to clip his nails and wings! We can't trust him with anyone but us three.
Chinchillas can also show similar behavior but probably not as extreme. My chinchilla is uncomfortable with being handled by anyone besides me and runs to me when he gets nervous out of his cage. I consider he is bonded to me. Otherwise he would show no preference. You'll usually see this when you get them from a breeder and at a young age like mine. Some chins take longer than others. By letting others handle the animal it can help but not always. Usually when we talk about bonding it occurs with the one or two people closest to it.
