I guess a better way of looking at "domestication" is the keeping of animals for multiple generations selecting for traits that make them more suitable to live around humans...
The only acceptable definition is a selectively bred animal with a genetic difference that better suits a human use, which I assume is what your definition means for the most part.

If the animal has a genetic difference but does not suit the purpose better than the wild starting point, it isn't domesticated in my opinion. Ball pythons for instance look different, particularly when they are morphs, but I think they are the same animals found in the wild. The key difference is the environment they are raised in. What many people don't consider is that animals are drastically different based on whether or not they are socialized with humans. Even domesticated animals can return to the wild. Here's something else to consider, domesticated dogs are often neutered and spayed, so we remove a chunk of their natural drive. Unneutered dogs are known to be roamers. Non-castrated camels are dangerous during the rutting season.
I theorized that many zoo animals have issues with pacing for being intact, and their sexual hormones are on fire. When an animal is fixed also plays a part. My vet told me if I didn't neuter my spotted genet early it might not make a difference if I do it later. I ended up not neutering him and thankfully he doesn't spray but he has extreme energy levels.

With my narrowed down definition I was finally able to understand which animals are 'domesticated' and which aren't. Cockatiels, parakeets, hamsters, gerbils, snakes, aren't.