Extinction is the elimination of a conditioned reflex or a conditioned response. These are generated when an environmental stimulus is applied to a naturally existing reflex or to a targeted behavior.
This said, one can make a conditioned response extinct when generated in either classical and operant conditioning.
In classical conditioning, conditioned reflex is extinguished when the environmental stimulus is withheld. The absence of the stimulus causes the generated reflex that reacts to the stimulus to gradually die out and become extinct.
In operant conditioning, the reinforced behavior no longer receives an environment stimulus (either positive reward or negative punishment) so the conditioned response, no longer reinforced, dies out or reverts to normal limits. In other words, when the conditioned response is no longer stimulated, even periodically, the conditioned response will become extinct.
The diminishing of a conditioned response (CR); occurs in classical conditioning when an unconditioned stimulus (US) does not follow a conditioned stimulus (CS) ; the diminished association between the UCS (food) and the CS (bell) after the UCS (food) is removed. The bell goes back to meaning nothing to the dog.
Occurs in operant conditioning when a response is no longer reinforced