Silly me, I try to come off as being laid back but fail miserably :)

Yes, Dire's right and I should've been quiet! Same old story here.

I usually consider any game whose scrolling rate isn't wholly independent of your avatar's movement (i.e. the game doesn't scroll by itself) to not be a shmup - be it a mech game like Xardion, Front Mission: Gun Hazard, or the Assault Suits series games; or a character-based title where you chuck stuff. I'd consider those action games.

On the other hand, where would you put Defender? Isn't that a (mostly) shooter? Then there's Atomic Runner (Chelnov), which only lets you stop running but otherwise moves you along at a fixed rate.

For me, then, the definition is found by looking at the game's main focus, like Dire said. If it's dodging bullets and shooting stuff, it's likely a shmup. If it's platforming or moving a humanoid character who controls mostly like a shmup does (Forgotten Worlds comes to mind) then it's likely best termed an action game.

On the old Mega Drive game boxes, it would be interesting to discover if Sega let companies choose whatever categories they thought fit best, did it themselves, or had a strict set of definitions (not so likely, I suppose).