The "old school" method of producing haze was to use a heater coil to burn a powder, sal ammoniac, to release particles in the air. Today, mineral oil or glycerin hazers such as the ReelEFX DF-50, Le Maitre Radiance, and many others, are used.
In this standards document, ANSI E1.23 - 2006 Entertainment Technology - Design and Execution of Theatrical Fog Effects, ESTA defines the terms thusly:
See also smoke, fog.1.3.2 fog: A mixture of liquid droplets in air that reduces visibility and reflects light.
1.3.3 haze: An accumulation in the atmosphere of very fine, widely dispersed, solid or liquid particles
giving the air an opalescent appearance.