Weigh in with your opinion and the industry standard to what constitutes a beauty, fashion, casual or head shot, and post some examples and reasons why.  Seems there area a lot of opionions out there.

Any opinions or thoughts from photogs or models?

Headshot to me means actor/actress.  No nonsense, show the client what an actor/actress is "going to look like when they walk in the door" photo.  Fashion is when the clothes take center stage to the model in the shot.  Usually over-styled (over the top of what you would wear walking down the street) and exaggerated.  Casual or sometimes called lifestyle shots is more about the model or the "feel" of the image. "Model in rocking chair-jeans-white shirt-drinking a cup of coffee" or looking more like a "mom" than a model.  This is sort of how we defined these things when I worked at the agency. 
Best Regards!
Amy

P.S. forgot to comment on the beauty shot.  Headshot usually for more of a fashion model with beauty lighting.  No shadows.