A beta animal is an animal that will act as a new alpha animal if the old alpha dies. In some species of birds, the males pair up in twos when courting, the beta male aiding the alpha male. The beta male does generally not get to mate with the female birds, but if the alpha dies, he takes over the alpha's females, becoming the new alpha.
Omega (usually rendered ω-male) is an antonym used to refer to the lowest caste of the hierarchical society. An omega is subordinated to all others in the community. The omega is commonly the last allowed to eat.
Sorry, but you're totally incorrect.
In the wolf/canine kindgom it goes as accordingly.
Alpha: The leader.
Beta: The one who follows the alpha, but if an alpha days will take over.
Omega: The instantly submissive.