nop, the two are completely unrelated.
you can use getAxis and getVectorAxis to do anything you want with it, it is not tight to controlling character at all. you could control your own controller for flying a plane, moving the camera, anything.
1: create a vector 3 fsm variable name "movement"
2: On a state, first have a "get Axis Vector" action and plug "movement" in the field "store vector"
3: on the same state right after "get Axis Vector" have the "Controller simple move" and plug "movement" to the field "move vector"
that is sufficient to control the character now.
BUT, you don't need a rigidBody attached to the character controller, this is not supposed to work that way. the characterController is a kind of a rigidBody already.