define-key upon common-lisp-mode and inferior-lisp-mode

[wilnerthomas]

Have encountered "common-lisp-mode" but there does not exist 
"common-lisp-mode-map".

Thusly  (define-key common-lisp-mode-map KEY DEF) fails
Also seen "inferior-lisp-mode-map". which has no associated 
"inferior-lisp-mode".  What is "inferior-lisp" and can one use it like 
lisp-mode?  Does it make sense to call "define-key" upon 
"inferior-lisp-mode-map"?