Think of "brawn" vs "brain" for the difference between the two.
Basically, a bodyguard's job is mostly show and intimidation. These are the guys (they're almost always men) you usually see in sitcoms, movies, and often with celebrities. The emphasis is on the size of the protector, which is why most of these men are very "big". Bodyguards are popular with many VIPs -- especially celebrities -- because Hollywood (sitcoms, movies, paparazzi pictures and videos of celebrities) has conditioned the general public to think size is important to provide protection to clients. Usually bodyguards' size is their main -- if not only -- attribute, and they usually have little to no formal training from a reputable executive protection school. In fact, they are sometimes the friends and acquaintances of their protectees, selected because of their familiarity with said protectee, despite their complete lack of protection training. They also rely primarily on deterrence -- their size -- to protect the client.
Executive protection (EP) agents perform the U.S. Secret Service type of protection. A vast majority of an EP agent's work occurs prior to any incident. Well trained EP agents are very proactive in their protective operations, which should be intelligence-driven. This means that when time allows, a considerable amount of effort is spent on assessing threats, vulnerabilities, and risks to the client and protective team. Bodyguards seldom prepare in this manner. EP agents are also trained to recognize and mitigate against reputation risks to the client. Often, bodyguards themselves pose a reputation (and also financial) risk to their clients due to illegally and unnecessarily confronting and attacking members of the public (e.g., fans, paparazzi, innocent bystanders). The marked difference in the level of professionalism between bodyguards and EP agents is why the latter are often reluctant to refer to themselves as "bodyguards".
Blue Glacier doesn't provide bodyguards. We provide executive protection agents.