Influenza is an infection of the respiratory system. Each year, the guys at the CDC, or whoever cooks up the flu shot, decide which strains are most likely to hit the US, and distribute a vaccine targeting them.
This flu season, due to the Anthrax exposures in October, there were wide-spread recomendations (by politicians; not by the CDC) that citizens get the flu shot. It was hoped that this would reduce stress by lowering the incidence of respiratory infections - the early onset of Anthrax infection and Influenza are apparently indistinguishable. And mostly gave people who were really stressing out about Anthrax, but actually at Very Low Risk, something positive they could do.
More in-depth information on the influenza vaccine is available here.
Respiratory infections can often cause gastric distress due to the increased mucous production and drainage. However, influenza is not "the stomach flu" and the many viruses that cause what is commonly called "stomach flu" are not targetted by the CDC vaccines.
More information on viral gastroenteritis is available here.
Okay, I feel better now.
Now to figure out how to put some of these things in memories...