You kid but back during the XEmacs days, RMS did indeed argue a lot over the names. I think jwz wanted to call the original Emacs "FSF Emacs" and RMS was like, "no, it's just Emacs, and in fact, XEmacs is also just Emacs" or something like that, I don't remember.
I'd just like to interject for a moment. What you're refering to as Emacs, is in fact, GNU/Emacs, or as I've recently taken to calling it, GNU plus Emacs.
Yes, and since `emacs` by itself is otherwise unbound to a concept, we've all done the shortcut of `(defalias 'emacs 'gnu/emacs)` in our mental .emacs files.