Well after years of calling Streets of Rage-Final Fight esque games Beatumups, someone turned me on to the term "Conveyor Belt Action" which is I guess what the Japanese call them. I really liked the name, so that's what I call them now.
I wonder what the Japanese call shmups... honestly I'm fine just calling them vertical and horizontal shooters but because of FPS you will just confuse someone when you tell them you love shooters.
I told someone I was really into 2d shooters and they said "what, like Doom 1?"