The fact that there are many implementations of Common LISP should be considered a good thing. In fact, given that there are roughly the same number of free implementations of Common LISP as there are free implementations of C++ is remarkable, considering the relative popularity of the languages.
Free Common LISP implementations include CMU CL, SBCL, OpenMCL / Clozure CL, CLISP, GCL and ECL.
Free C++ implementations include G++ (with Cygwin and MinGW32 variants), Digital Mars, Open Watcom, Borland C++ (legacy?) and CINT (interpreter). There are also various STL implementations for C++.
With regards to Scheme and Common LISP, although admittedly, an inaccurate analogy, there are times when I would consider Scheme is to Common LISP what C is to C++, i.e. while Scheme and C are small and elegant, Common LISP and C++ are large and (arguably) more suited for larger applications.