Shoot-'Em-Up: Shooting action games in a 2D overhead, side, or top-down perspective against a large number of enemies while dodging their fire.
Examples: Gradius, R-Type, Deathsmiles, Smash TV, Geometry Wars, Super Stardust Delta, Space Invaders, Galaga, Ikaruga
Do people have a different idea of what shmups are? I generally think of them as how you described it.
While editing I have run across some games incorrectly categorized as Shoot-’Em-Up. Usually they are first- or third-person shooters. In general, it’s been a game that has a weapon capable of rapid fire. On a couple of occasions I ran across Action RPG’s categorized as such.
As for Beat’Em-Up, I’ve seen one-on-one unarmed combat games and even boxing games with this genre attached to them. Action RPG’s too!
Ah, I gotcha! I'll have to keep an eye out for that when I'm checking over records/edits