Emacs Lisp is similar to CL, since both were derived from Maclisp and many basic code looks similar.
In Common Lisp a subset would mean that all programs of that subset would run unchanged in a full CL implementation. Emacs Lisp isn't like that.
More tragically, over time, Emacs Lisp implemented Common Lisp features - even though Richard Stallman does not like Common Lisp's features like keyword arguments - but not in a source compatible way. Emacs Lisp got CL features and operators via libraries, often with incompatible naming, but still can't be programmed in straight Common Lisp.
In Common Lisp a subset would mean that all programs of that subset would run unchanged in a full CL implementation. Emacs Lisp isn't like that.
More tragically, over time, Emacs Lisp implemented Common Lisp features - even though Richard Stallman does not like Common Lisp's features like keyword arguments - but not in a source compatible way. Emacs Lisp got CL features and operators via libraries, often with incompatible naming, but still can't be programmed in straight Common Lisp.