Classical conditioning involves the pairing of an unconditioned stimulus and conditioned stimulus to elicit a conditioned response, discovered by Ivan Pavlov in the early 1900s. Operant conditioning, coined by B.F. Skinner in 1938, explains how behaviors are modified by consequences like rewards. The key differences are that classical conditioning involves stimulus pairing and association, while operant conditioning involves response modification through consequences without stimulus pairing. Classical conditioning results in reflexes, while operant conditioning shapes external behaviors controlled by the central nervous system.