Pets are domesticated. My two himalayans wouldn't last 5 minutes outside. If you've ever observed the behavioural differences between an alley cat and a purebred, you'll know what I'm talking about.
Short anecdote: We used to have a shelter cat, he was a kitten when I got him, I've posted pictures of him on here, he was beautiful. Probably came out of a barn litter or something, ended up at the humane society and that's where I found him. Fantastic hunter, could catch bats out of mid-air in the house when we had the odd one slip-in. Now, the two idiots while he was getting old, and they were quite young, would just watch him. They hadn't the faintest of clues as to what he was doing. They had absolutely no interest in catching the bats; zero hunting instinct. My kids have a couple of hamsters, the himmies just sniff them, the old boy would have tried to turn them into a snack.
All three the cats were raised the exact same by me. It's an instinct, it's bred-out of a lot of breeds as part of process. Many of the animals we call pets are not naturally wild animals in most cases. Dog breeds are all creations, some with centuries of lineage. The same goes for many cat breeds.
Speaking of birds and survival, climate plays a huge role. Yeah, a parrot or some other tropical bird would be dead right now up here, but it's not because it doesn't have its parrot buddies to snuggle with, it's because it's not from Canada and isn't equipped to handle winter. Animals have adapted to their natural habitats, it's humans that have taken them out of those locations for the purpose of keeping them.
Truly wild animals taken as pets can be wildly unpredictable. Look at folks that have kept lions and tigers and gotten mauled, often killed. The same goes for bears. Racoons can be really sketchy and are wickedly clever. There's a massive difference between my old Newfoundland, a dog that is a product of man's breeding practices, and somebody picking up a bear cub and deciding to take it home and call him Fred. The temperament of domestic dogs is part of the breeding process, it's one of the traits honed. We produce dogs that behave a certain way and what that looks like will depend on the breed.
So, pets are different. Domesticated ones that is. They are mans creation, a manipulation of nature for companionship and utility.