Don't you consider these games that scroll "up" a different genre than ones that scroll to the side? (As you would say, "obviously".) I may be confusing you with someone else, but I never could understand that, considering you can literally "genre shift" by tilting your TV on its side.
"On two occasions, I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able to rightly apprehend the kind of confusion of ideas that could provoke such a question." ~ Charles Babbage (1791-1871)
Well, shmups are usually broken down into the vertical-scrolling ones and the horizontal-scrolling ones, but both are kinds of shmups, so I'd say they are the same genre... but yeah, those are the two main categories of the genre. A few games have both directions in them (Life Force/Salamander, for example, or Axelay), but most stick with one or the other.