I guess the first question to clear up is ‘what is a headshot?’ For most people there is a tangible difference between a headshot and a portrait, therefore it is important to clarify this at the beginning. The content below is drawn from Wikipedia because I couldn’t have put it much better:
A head shot or headshot is a specific type of portrait (usually a photograph) that realistically demonstrates a person’s appearance for branding or casting. Many head shots are promotional pictures of actors, models, authors. Headshots could be a portrait of a face or full body with a background that clearly illustrate the personality inside the person photographed.
Modeling head shots or comp cards, sometimes also called tear sheets, are a compilation of images for casting in one sheet with a résumé of work, name and relevant statistics. They are often done in color; however in some jurisdictions, such as the UK, they may be in black-and-white. Models often use them for castings and modeling work applications. A close-up head shot is often required to show a model’s skin complexion for beauty work.
Corporate head shots are portraits often produced digitally and used for engaging in social media, the ‘about us’ page and industry specialty sites. A headshot or head shot is often used for branding and to showcase the business leader’s life, style and personality while corporations will use the headshot to merge branding between the people working for them and its agency. Traditional head shots are still taken in a studio setting, though shots “on-location” or “in-the-field” continue to increase in popularity. In both cases, backgrounds tend to be simple. Subjects are often shown head-to-chest or head-to-torso.
Source – Wikipedia
So, in essence a headshot is a subset of portraiture, usually simpler in form, often with a plain background. We shoot both portraits and headshots, occasionally the line between becomes blurred.