I hear at least two of these terms thrown around on here, so I'll put in my own two cents on this based on observation. (also I use straight/hetero terms in here feel free to replace them with other pronouns based on YOUR orientation). Warning this is just a general for fun view, not a fits all post.
Alpha Male- Light side-The Leader, Dark side-The Tyrant
Alpha Males are the stereotypical manly men. Physically powerfully and emotionally void, they lead without question and are warriors at heart. However they can be stubborn and tyrannical. Dating one can be tricky for not completely submissive women as Alphas seek to rule and control. They tend to go for physically weaker and smaller females. Seductive and charming it's easy to fall into bed with one only to not fully like his brutal, domineering style of sex. They are also staunch traditionalists and thrive of preconceived gender/sex roles. Also can be critical of flaws.
Beta Males- Light Side- The Team Player, Dark side- The Envious One
Beta Males strike a more feminine version of a male. Quick, cunning and physically weaker they have more of a mental attraction. They can be more compromising then Alphas but also harbor grudges more often. Dating one can be easier for dominant women then submissive but can be maddening at the Beta's lack of initiative and waffling of opinions. They can swing between traditional and progressive views easily. Can be critical but less so then Alphas.
Omega Males- Light Side- the Unique one Dark Side- The Rebel without a Clue
Omega Males are a breed all their own. They tend not to put emphasis on their or their partner's physical features looking for more mental/emotional similarities. They live for compromise with a partner but shun society's views. Dating one is an adventure for any women but rare because very few Omega Males seem to exist. It can be hard if you want to fit in though as Omegas hate the crowd. Usually gender roles are eschewed. Not as critical as Betas or Omegas. 
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