You're not exactly wrong, but you are oversimplifying to the point where 'correct' is lost.
"Classical" conditioning is about stimulus-pairing. This means that I start to associate X with Y. I.e., this type of food with stomach illness (in the 'sparkling water' experiments). THIS REQUIRES NO ACTION ON YOUR PART. It's not really 'behavioral', in the sense that I'm not directly interacting or affecting your behavior - just your psychological associations. Obviously behavior will be indirectly affected here, since if I think "sex is bad," I'm going to start avoiding sex (ha, as if.)
Operant conditioning is about modifying your behavior - I am directly reinforcing or dissuading certain actions THAT YOU TAKE. Think 'operant' in that the subject must be the 'operator' - they must be doing something, which can then be affected. This isn't about stimuli; it's about behavioral modification.