A headshot is what the word says it is - a shot of a head :-) Simple as that. So why not call it a portrait?
Portraits most often tell a story; a watch maker with his watches, an author with his books, jockey with horses, etc. and therefore has multiple messages to send to you
A headshot only has one message: YOU and the person you are (not what you do)
This is IMO the most important difference - lighting, studio, equipment may be exactly the same but focus is different
For the headshot, the only focus is you, your expression and how well you convey yourself to the viewer - which actually makes the headshot somewhat more difficult to make - here are no props (watches, books, etc.) to play with, to keep the hands busy and to take focus away from the fact that you're being photographed
There's only you
For a headshot to be world-class, it has to convey you. It has to show you as you are; confident, approachable, cool, friendly, etc.
And this is what separates a headshot photographer from a portrait photographer; the uniquely and dedicated (some say obsessed) focus on you, your looks, your personality's message and your expression the moment it clicks
All I want is to make you look the very, very best