A Lisp Machine is a real computer with a Lisp OS, applications, libraries and tools. An editor is just a part of that experience. But not the central part. Typically the environment of Lisp Machines was NOT written around the editor. They had a window/mouse/GUI oriented user interface with a lot of support for keyboard use. If you take for example the Lisp Listener in Symbolics Genera, it is not a Zmacs application and it does not use Zmacs in any way - other than that you can switch to Zmacs windows.

GNU Emacs is an editor written in some more primitive Lisp with extensive libraries and applications. It lacks the extensive low-level features, multi-threading, Flavors/CLOS etc of Zetalisp or Interlisp. GNU Emacs implements all their applications inside the editor. Lisp Machines did not do that.

If you've ever used a Lisp Machine, the look&feel was quite different from GNU Emacs.