Influenza produces symptoms similar to the common cold, which can include nasal and chest congestion, coughing, sore throat, runny nose, chills, and fever. Despite similar symptoms, the flu is caused by influenza viruses (family Orthomyxoviridae) and the common cold is caused primarily by rhinoviruses and coronaviruses (families Picornaviridae and Coronaviridae, respectively).
“Stomach flu” is also commonly referred to as “The Flu,” but it is entirely different from influenza. This illness is gastroenteritis, which commonly produces diarrhea, nausea, and vomiting. Caused primarily by noroviruses (family Caliciviridae), the infectious agents, diseases, and symptoms are entirely different from those related to influenza and cold viruses.
I’d really like to see people restrict their use of “The Flu” to influenza and call “stomach flu” something else entirely to avoid confusion. I prefer referring to “stomach flu” as a norovirus (although it can also be caused by rotaviruses, adenoviruses, and astroviruses). Gastroenteritis would also be acceptable.