Interestingly (for some of you anyway!) the name smoke machine is not strictly correct for consumer effects units, as the official definition of theatrical effect smoke is solid particles released from a combustible, so is only true of pyrotechnics and other solid flammable substances.
The machines we know and love are actually all variants of the fog machine, which came along during the mid 1980s as a safer alternative to using dry ice and nitrogen based units on film sets which were fairly hazardous both in use and storage, and would present health problems with continued exposure.
These modern machines use liquid made from a mixture of water, mineral oil, glycol or glycerin, which is fed from a tank via a pump into an electric coil heat exchanger. The liquid is then vaporized by the heat under pressure and forced out of a nozzle.
Its this exact set up in miniaturised form using glycol based liquid that is now being used in Vape electronic cigarettes.
Variations in heating element power and pump performance are the main reason for differences in price and physical size, with small home or light Dj use units starting at 500w and featuring small to medium sized liquid tanks of 250 or 500ml, which is plenty of power and fluid for an average night of timed bursts.
Moving up to a unit that's required to be in constant usage all night, the heating element goes up in power to anything from 700w up to 2000w, with fluid reservoirs of 2 or 3 litres, and on the largest units the ability to drop a 5 litre container straight in.
Having a larger rated heater element and pump isn't just about bigger fog output, although this obviously is a factor. The larger unit can cope with being up to temperature for extended periods of time, so can function consistently for an entire event, whereas a smaller unit cools down after firing and needs a certain amount of recovery time before it's back to full temperature. You also get better atomisation from a more powerful unit, so the output nozzle is less prone to spitting out un-vaporized fluid which can happen on cheaper low power systems.
Low fog or dry ice machines are exactly the same, just with onboard ice storage and fans to produce the low level effect. The larger the machine, the more fluid and ice it can obviously hold, and the larger the internal fan can be. Fog and ice machines are generally higher power anyway, as the nature of the unit demands its output to be high volume capable.
All smoke and fog machines will at least come with a remote control for firing, with some larger units having timer control. Higher end professional units will feature DMX connectivity so remote firing can be programmed or timed as part of show set up, allowing full integration into a pro mobile or installation rig.