What is an Alpha Male?
Everyone online is a self-proclaimed alpha or rising beta. But if you think there are short-cuts to the status (i.e., enthralled by the impostor strategies of PUA "game" charlatans and nothing more), you've already demonstrated your relative rank. Nature gives us apex predators, pack leaders, and "kings of the jungle" whose force of will binds inferiors together. She also gives us mimics, scavengers, parasites, nocturnal thieves, saboteurs, and drones whose weaknesses are finessed into a survivable modus vivendi. The least aware among the social dynamic want to wedge their antisocial predilections into "alpha" for purposes of false dignity. It's a very human tendency, and one that should be disabused at every turn if there is to be any integrity in the idea of "alpha."
Being an alpha has to do with one’s involvement in a group. More specifically, it’s about helping develop and maintaining a group dynamic, hierarchy and the functionality of the group. Before you can understand what an alpha is, you first need to understand something about the nature of power. Namely: Power is granted to you by the group. You don’t have power unless other people give it to you. Here’s the catch, the group gives you power on the condition that you look out for their needs. That’s the deal. You get extra power to serve them. If you violate this trust then you will be stripped of your power by the group. Too much self-indulgence and not enough leadership will eventually get your ass kicked by the people you used to lead.
The PUA schtick is: "Women want to mate with the local alpha ... and while it's hard to *be* the local alpha, it's pretty easy to fool the dumb bints with a few mannerisms and behaviors." So actual alpha status gets conflated with alpha status *in the eyes of one or more women* with the *sexual fruits of alpha status*. Nothing (or not much) that you wrote is wrong, just a little besides the point.
A beta animal is an animal that is second-in-command to the reigning alpha and will act as a new alpha animal if the old alpha dies.