I only got into Emacs last year or so, but I’ve never used anything but company-mode. I’m also curious if this is what they are talking about or if there’s something else I’m missing.
They are talking about frameworks leveraging and extending the builtin Emacs completition mechanism [1]. The most well known ones are Ivy and Helm, I believe, but there are now many others.
I realized this after it was too late to edit my comment. Apparently a year of using Emacs is not enough to stop confusing “completion” and “auto-completion” in my head..