Not-so-simple explanation though technically correct, since most people will have come across 'steam' every day as hot gas + condensing water vapour = white cloud, whereas not very many people will ever have seen 'pure' steam without the accompanying droplets. (if its invisible, no-one can see it...)
hmmm --- reminds me of the BBC road weather alert I heard one morning when living in England: "Watch out for black ice on the roads today, because you can't see it!"
Steam is invisible. So, technically, is water vapour. In both cases they are gaseous water, and gaseous water is a colourless, odourless, and invisible gas. The usual distinction is that above 100°C -- boiling point -- you call it steam; below 100°C you call it vapour.
But in everyday language both steam and vapour are terms applied to a visible aerosol of water droplets that is formed when gaseous water condenses back to a liquid.
Mist can be a meteorological term for a very fine rain that falls slowly in a ground-level cloud. It can also be a term that applies more generally to any liquid aerosol (very small liquid droplets in a gaseous medium).