As long as a pet is captive bred and has been well looked after since birth I believe it will always want to be cared for and provided with food and attention. Most stray and homeless animals are happier when they are rehomed by a loving family.
Cats, dogs and horses have been domesticated for millions of years, so human companionship is natural for them. I think it might be different for a non-domestic animal. I mean exotic pets that have been taken from the wild, or are descended from wild animals.
Pet mice need care and attention, and they respond to humans, whereas a wild mouse would not like to be kept in a cage and would only want to get back to the wild. Pet birds panick when they escape and end up being rescued. A wild bird will fly to freedom and never be seen again.
