The problem is that both CL and Scheme communities have very little to do with each other.
For practical purposes Lisp dialects are those directly inheriting back to Lisp I from McCarthy. You can run programs from 1960 in Common Lisp with very little changes (unless it uses machine interfaces). To port them to Scheme is possible. To port them to Logo, Clojure, Javascript or other languages considered to be dialects in a wider sense mostly means a rewrite.
Thus for me Lisp means the dialects of Lisp and their respective communities which can share code, libraries, applications by relatively simple ports. For example Emacs Lisp has Common Lisp enhancements, which are semantically very similar. ISLISP could be directly integrated into a Common Lisp - Kent Pitman mentioned that he actually did that to see that they are culturally compatible.
Languages who don't directly share code are maybe part of an abstract family, which has no agreed on definition - thus this is for practical purposes relatively useless.