To simplify, a professional headshot is a type of portrait. A headshot is a tightly cropped photo of the face, from the shoulders up. The subject is typically looking right in the lens.
I headshot can be used by actors and models for their portfolio, by realtors, brokers, lawyers and many more. A good professional headshot can be used for personal purposes as well. Don’t forget about online dating profiles, blogs, social media etc.
A portrait is a much broader term. Essentially any image where the subject is aware she’s being photographed, even if she’s not looking at the camera.