Haze machines and fog machines change the dynamic of a light show. Rather than just projection lighting, a small amount of haze or fog in the air will allow you to create an aerial lighting show with visible beams of light thru the venue.
Hazers are typically better at creating a thin coverage that may not even be visible in the room without a light show, as they offer a steady stream of light haze. While foggers output short bursts of fog, which is typically thicker. A fazer is a hybrid as it's technically a fogger that acts like a hazer with constant output.
