While the regular fountain re-circulates the water to provide relaxing sound, the mist fountain takes it to a different level by employing the use of ultrasonic pulses to create the fog or mist.  Here's how it looks:

Basic Operation

It’s not like putting a block of dry ice into a basin of water to produce the mist. Inside the fountain is a built-in electronic module. This module produces vibrations in the water at a frequency of 1.7 million pulses per second. The rapid vibrations send water molecules into the air. The water vapor trapped in the air creates the mist or fog and the water vapor evaporates adding humidity to the air.

How is the rapid vibration in the water produced?

Piezoelectricity produces the vibrations in the water.

Piezoelectricity is the ability of some materials like crystals and certain ceramics including bones to generate an electric potential in response to applied mechanical stress. Ref: (Wikipedia)

The electronic module built in the mist fountain uses a small nickel or titanium coated ceramic disk. Piezoelectric effect is reversible. A material having direct piezoelectric effect can also have the reverse. That is, it can either produce electricity when stress is applied or it can produce stress when electricity is applied. In the case of a mist unit, high frequency electric field is applied to the ceramic disk from the electronic module resulting to the rapid vibrations under the water producing negative ions (anions) and mist.(minute particles of water suspended in the atmosphere)

The negative ions produced were found to reduce dust in the air by 52% and bacteria in the air by 95% according to the U.S. Department of Agriculture.

Using Water:

It needs to be entirely immersed in water for the misting unit to operate. The piezoelectric disk would likely be damaged if electric field is applied while the unit is not immersed in water. However, all electronic modules are built with a low water sensor that determines the conductivity of water; meaning no water, no current would flow to the ceramic disk. Distilled water is not ideal or advisable for use in the mist fountain because the dissolved minerals in the water are no longer present due to the purification process making it a poor conductor of electricity. The low water sensor would not work even if it is immersed in water.

High-power mist units come with 3 to 9 separate ‘misters’ for bigger applications like ponds, streams and other water structures in your yard. The later models of mist fountains are built with LEDs of different colors aligned around the edge of the module which intensify the beautiful effect of the mist fountain. The LEDs are controllable in many ways to change your color preference in a variety of color combinations.

A mist fountain works well in a place where there is enough air circulation to allow enough evaporation, that serves its purpose for humidity.

Like any household appliances, you need to clean the mist fountain regularly primarily the water in the reservoir or basin. This will prevent bacteria build up which may later cause air pollution in your home instead of a clean and healthy atmosphere.