Dance clubs are aimed at people who want to dress up, socialise, and dance. They are often very large, attracting many hundred of people. Good examples of dance orientated clubs are Torture Garden and Club Rub.
Play clubs on the other hand tend to be smaller and geared towards people who enjoy scening in public. They often do not have a dance floor and whilst most enforce a strict dress code the costumes are not as outragous. Good examples of play clubs are The Gate and Sweet Torments. They tend to have a much more of sexual edge about them.