If we are talking about 'spectator' (singular), the difference is that we can talk about one spectator, but an audience is a group. For plural 'spectators', the biggest difference is that 'spectators' refers to people that watch (a sporting event for example); 'audience' is a group of people that watch and listen, probably to a speech or concert. If I was talking about the people at a speech, I would talk about an audience. At a circus, you could use audience or spectators, probably audience. Soccer game - spectators. People gathered around a car accident - spectators Play or film - audience.

A spectator comes to look at or watch somethng. An audience is there to listen to something. This is a very general rule and there are always exceptions to English rules.

The audience is a set, whose members are the single spectators.