There are a traditional styles of headshot photography where a formula is followed which requires a type of lighting, posing and a particular setting. The more contemporary style of headshot follows a magazine style of portrait, which still requires lighting, posing and a particular setting, however it can vary.
Either style of headshot is valid and is driven by the business or the individual and the look they want to portray. A law firm for example will proably want something traditional to appeal to the clients they are trying to attract. A young entrepreneur with a contemporary start up will be after something leaning towards a different style. Think about a personal trainer and the style of headshot they might want. its going to be different again from everything above. There are no rules.
The setting, lighting,posing clothing and makeup are some of the elements used to create the style of headshot the client is after.
With a consultation its the photographers job to work out the story that is to be told with each headshot.