Most of what are termed fog machines are technically smoke machines. Barco/High End Systems F100 is one such machine. A chiller module, using either liquid or solid CO2, may be added to chemical smoke machines to produce fog.
There have been many threads on CB about building one's own dry ice fog machine (just type "dry ice" into the search box): http://www.controlbooth.com/forums/special-f-x/10395-dry-ice-question-4-2-million.html, http://www.controlbooth.com/forums/special-f-x/3636-building-dry-ice-fog-machine.html, http://www.controlbooth.com/forums/special-f-x/9225-dry-ice-fog-machine-tips.html.
For a manufactured product, see City Theatrical's AquaFog3300. For solutions using liquid nitrogen, see the site: Interesting Products. See also this UK site: http://www.smokemachines.net/faqs.shtml, from the makers of the Peasouper dry ice fogger.
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, haze.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.
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