Well I'm no expert but the NS-Tower and NS-Shaft were shareware games released in 1996 on Macintosh PCs and later Windows in 1997 by Nagi-P Soft. They were Nagi-P Soft's most popular games so they occasionally received free updates and the company continued to distribute these simple games for over 20 years across many platforms. As early as 2003 the games were made available on mobile phones and the same year Nagi-P Soft licensed the Aleck64 arcade remakes, which eventually got updated GBA ports in 2004 in Japan. So yes these games have striking similarity because they are supposed to be the same series. Just about every early 2000s cell phone probably had these games pre-installed on them
Not sure what you would call the genre, but if you google vertical platformers or vertical scrolling platformers that's what most people call them. Nowadays they are quite common in the indie space with games like Towerclimb and Downwell but they are both much more complicated. I can think of many games before 1997 with vertical sections or levels. Kid Icarus is almost all vertical but it doesn't scroll automatically or anything. Not sure what the first game that was all vertical autoscrolling would have been, probably some games on home computer systems had to have tried something similar
