I've had a few respiratory bouts that were definitely the real flu. I've only once that I can remember had viral gastroenteritis, or "stomach flu."
Back to the respiratory, or "real" flu, many people don't know that quite a few different flu viruses are active in any given year. Vaccine producers watch the trends carefully and project which three viral strains are most likely to cause serious epidemics, and those three go into that year's vaccine. The vaccines are not 100% effective, especially in the elderly or immune-compromised, but they do generally lessen the impact of the virus, and they do impart considerable "herd immunity," that is, if enough people in any population have had the vaccine, there are fewer cases of the illness being passed around to everybody else.
So vaccinated people can still get the flu, but have at least partial protection against the greatest threats in any given year. And I value that protection mightily, because I've had lifelong asthma, and recently have also become diabetic. The last two bouts of flu I contracted, though relatively mild themselves, required expensive treatment for secondary infections.