Domestication is a result of animal husbandry where the humans consciously only allow animals to breed that have desirable traits, such as gentleness and submissiveness.
Animals with undesirable traits are either killed or not allowed to breed, so those genes are not spread to successive generations.
This process requires many generations over hundreds or thousands of years.
Certain wild animals, such as parrots, have been kept as pets for a hundred or so years, but still retain all of the traits of their feral counterparts.
They are not domesticated, but have learned to trust, to a certain extent, the humans around them.