The flu shot does is not for norovirus. It is for influenza which is completely different.I remember having bad flu ages ago with the necessary swapping ends at the porcelain bowl. Having good timing I was able to hit on target from either end - thankfully. Flush and then reload. It was still awful.
Flu shots made that a distant nightmare.
It is confusing but maybe if you call it stomach flu? The other could be called influenza flu?