Another implementation of Emacs, called Multics Emacs (since it ran on Multics), innovated the notion of using Lisp as the programming language for implementing Emacs. The version of Emacs implemented by James Gosling (commonly known as Gosmacs) came directly from Multics Emacs. Richard Stallman's GNU Emacs has Gosmacs as its ancestor, and from GNU Emacs came XEmacs. Most Common Lisp systems implement their own idiosyncratic and non-portable Emacs, such as CMUCL's Hemlock.
For an extensive collection of information about various Emacs implementations see Craig Finseth's Emacs Implementations and Literature. Craig Finseth also has an excellent treatise on the implementation of Emacs-like editors available for free in HTML format, The Craft of Text Editing. It is required reading for any Emacs implementor.
Work is very slowly progressing to design a portable Emacs based on Common Lisp, (and maybe even CLIM) rather than the idiosyncratic and aging Emacs Lisp dialect, elisp, that all Emacsen deriving from GNU Emacs use. Take a look at CL-Emacs for more information.