A good definition of domesticated is an animal that never reaches emotional maturity. Instead they emotionally remain in preadolescence.
But this selective breeding never entirely controls them, a big reason that pet neutering is used.
Context is also important to domestication. A dog behaves very differently with his human owners than he does in a dog pack. The same with domestic cats, with people and with a group of other cats.
There are also types of domestication, such as the differences between horses, donkeys and mules.
Horses naturally live in a very hierarchical herd arrangement, and can adapt to having a human leader. Donkeys are generally loners, though female donkeys will often band together out of friendship. And this is the same with their relationship with humans. They do what you want not because you order it, but because they like you.
(Importantly, in the wild, both horses and donkeys can be quite violent to perceived threats, like wildcats and coyotes.)
Mules, a cross-breed of horses and donkeys, are a pain in the butt. They neither take orders nor do they like you. So forcing them to comply needs considerable force and bad language, done by rare mule experts called muleskinners.
They are far stronger than donkeys, less prone to illness and extremes of climate than are horses, and they are not picky eaters.
But again, horses, donkeys, and mules are all technically “domesticated”.
Is donkey another name for burro?