This comment section has made it clear to me (and maybe others that use some of these tools every 10 years) that just finding the correct project/binary if you want to use TeX can be... interesting :)
I recently co-authored an article [0] that attempts to explain the various engines and formats.
My personal recommendation would be to just always use "lualatex", or "pdflatex" if you have older documents that won't work with LuaLaTeX for some reason. I'm also a big fan of ConTeXt [2], but I realize that that isn't a practical option for most people.
https://www.tug.org/levels.html seems like a good start