In this instance it was for a business card, but had it been for a website I would have started asking questions to see if an environmental photo would work better. An environmental photo isn’t as tight as a headshot for the purpose of the background, and what is in it, informing the viewer about the person in the picture. these pictures work well for a website because there is often a lot of space to display the picture and an environmental photo is more personal and visually interesting.
If it was for a brochure for an event then I would lead off with questions about if there would be headshots of other people in the brochure. My goal here would be to find out if there is a general style that these headshots are supposed to follow to help make the brochure cohesive. I would also try to find out who is putting out the brochure and talk to them.
If it was for an actor/actress then the term headshot takes on all kinds of meaning.
In all instances I would be asking about the look of where the headshot would be published. In this specific example the head shot was for a business card that would have a monochrome look. It was to be powerful, elegant and bold.
The important thing is that, no matter the type of picture, your photographer should be asking you questions not only to find out what you want, but also what you need.