There are implementations which implement the standard, slight variations of it (lower case identifiers, ...) or large extended versions of it (+ MOP + CLOS everywhere + ...).
There are also derived languages like Stella, L, SubL and others which implement some kind of subset.
Then there is ISLisp, which is very similar, but slightly simplified.
Common Lisp is a member of the Lisp familiy of languages, just like Clojure is.
[1] http://www.cliki.net/Common%20Lisp%20implementation
[2] http://en.wikipedia.org/wiki/Common_Lisp#Implementations