Stand-up comedy is on stage, in front of an audience. A comedian can be 'stand-up' or just a regular comedy actor on a movie or tv show, or both. Jerry Seinfeld started as a stand-up comedian before going into TV shows. Most of the really good comedians started their career as stand-up comedians

Stand up comedy is the name given to the performance of a comedy show where the comedian stands behind a microphone in front of a live audience or simply performs to a live audience. Whereas a comedian, someone who performs comedy, can feature in a film, tv show or some other medium not in front of a live audience. Hope that helps you.