I remember when STR8UP used to post here he was fond of alpha-posturing towards the end of his tenure. In one particular thread we were arguing over the contextual basis of alpha-beta; he contended it was more of an absolute state of mind you develop and I contended it was situational and relative. So I said to him, "Str8up, if I saw you on the street and decided I wanted to manhandle you into a dumpster---simply because I'm bigger and stronger and I dont like you---who is more "alpha", in that moment?"
It's all about CONTEXT, and perception. As Zekko was saying, a man can be an alpha in the office, or in the gym, or on his team; yet still be a complete beta with his wife. Conversely he could have a really healthy, dominant frame with his wife, yet be the lowest man in the totem pole at work. A PUA can alpha-posture his way into (some) women's pants, or he might simply be in a natural alpha position because of excellent looks, charm, money, etc.
Similarly, a guy can be a beta provider in the sense he makes the bacon but his wife runs the show, or he could be an alpha provider in the sense he is still the majority earner but with that also has the respect of his family and has assumed a position of leadership. If a man does not assume that position, the women will either leave, or more likely fill that void herself.
Alpha-Betaisms are at best a limited teaching tool and more often just another form of jerk-off semantics used to stroke egos.