A spectator is someone that is looking at an event. It can be any event, a game, a sporting event, a play, a movie, a speech etc. the only requirement to be a spectator is that you actually "see" the event and do not participate. An onlooker. An audience is a group of people who witness a public event, a group of people who listen to, view or read something made for their appreciation, or the granting of a meeting with or interview by an individual (such as an audience with the president). All spectators are part of an audience. Not all audiences have spectators. For example, the community of people who use italki.com are the audience for your question. We are not spectators.

Audience is gathering of persons for the purpose of hearing a speaker, a singer etc. Spectator is an onlooker( esp at a show or game)