A producer uses software and analog equipment to superimpose sounds and instruments on top of each other to create music (and some of them develop the work of other artists). A DJ is a live artist who mixes ready-made music to play before people at clubs, parties, and other gatherings. In short, a producer is someone who makes music. Whereas a DJ is someone who plays music for the crowd.
While often an artist will be both, most superstars certainly are. They tend to pay special attention to aspects such as the tone and the way in which they are affected by different instruments and programs.