Difference between Classical and Operant Conditioning

In classical conditioning a stimulus that already leads to a response is replaced by a different stimulus. In operant conditioning a behaviour is picked out and either reinforced or punished to make it more or less common. So you could say one acts to modify or replace the stimulus that leads to a given response, and the other to modify or refine a response.
In terms of Pavlov's dog (classical) this meant replacing the smell of food, as the stimulus that leads to salivation, with the sound of a bell instead so that eventually even with the sound of the bell alone the dog has 'learned' to salivate. In terms of Skinner's cat (operant) the stimulus was confinement and the natural behaviour was to explore the environment for an escape. Teaching the cat to press the lever to get out can be seen as refining this behaviour with a reward. Here, of course, the cat was not shown how to press the lever. It discovered it randomly on it's own. But thereafter it did not waste much time before pressing the lever.