From a physics perspective, is there a difference between fog and steam? What is it and how does is manifest in properties of fog vs properties of steam?
Steam is water in a gas phase, while mist, or fog, are small droplets of water in the condensed phase, but small enough to be kept in the air by thermal Brownian motion. There is a huge difference in their properties.
steam at 1 atmospheric pressure is defined to be water at a temperature of 100 degrees celsius or more. It is an invisible gas, and contains a large latent energy which is released when the steam condenses into droplets. It is highly dangerous, since its high energy content can scald very effectively per unit mass.
Mist, on the other hand, is a harmless droplet state with only marginally more energy than bulk water. The extra energy is all due to the surface tension of the droplet formed, and is orders of magnitude smaller than the latent heat required to boil water. To make a mist or a fog, you can charge water electrically, and the electric repulsion will form droplets for you.
Humidity is water dissolved in air, and it is a different issue. Air will come to statistical equilibrium with liquid water when it has a certain water content, defined as 100% humidity. At any lower level, water will evaporate into the air, and at any higher level, water will spontaneously condense into droplets in the air.