Well, these genre names are rarely chosen intelligently. People were initially just saying that certain games are like Rogue, and that eventually just started to include more and more. In recent history, we've also had "Souls-likes" which started out similarly innocent.

I mean, sometimes there's a relatively intuitive name that people standardize on, like "Jump'n'Run", but that wasn't really possible with Roguelikes, as people hardly knew which parts of the Rogue formula were genre-defining.

Well, and it's also just a rather abstract genre. Even retrospectively, we could only really call it "Permadeath'n'ProceduralMapGeneration".

Rogueli*es

Likes are a pretty strictly defined genre. Lites on the other hand can be almost any genre. You could categorize both as "Run based games" but that leaves you with a very vague definition that says almost nothing about a game except that it´s ... run based.

There basically is. "Run based games". Stuff like FTL also fall into that category.

But also? Just because you like Stoneshard doesn't mean you like Shortest Trip to Earth. Just like how "action games" covers pretty FPS and TPS and Platformers. Or how "FPS" covers arena shooters, Call of Duty, and milsims.