In the modern world there basically is only GNU Emacs. The only other actively maintained editor (well, there's Linus's microemacs tree too I guess) that calls itself "emacs" is XEmacs, a long-time fork of GNU Emacs. But it's been fading steadily over the past decade and at this point very few people use it or even know about it.

Basically: yes, you can be unambiguous by just saying "emacs" and everyone who cares will know exactly what software you use. But for the same reason it's not really correct anymore to use "emacs" to refer to a "general class of editor". You need to be more explicit if you're invoking historical or oddball variants.