"Steam" is very definitely the gas phase of water. Water vapor is too. If we are talking about chemistry they are essentially synonyms.

If we are talking engineering, the term steam generally implies water vapor that is at or above the saturation temperature.

In every day usage they are usually drawing a distinction between visible and invisible water vapor, usually caused by the presence of liquid droplets, with "steam" being essentially "fog", but hotter.

"Steam is liquid water droplets suspended in gas": You clearly did not work on steam-powered ships (or land-based steam power plants). I was Main Propulsion Assistant on a steam powered destroyer, and I can assure you that every effort is made to prevent droplets being suspended in the steam--because such droplets erode the blades on steam turbines. To that end, steam coming out of the stem drum (the upper part of the boiler) is run through superheaters, which raise the temperature of the incoming steam to evaporate any droplets. On our ship, the steam coming off the steam drum was a bit over 1200 psi and 600 some degrees Fahrenheit. After it goes through the superheaters, it's about the same pressure but 975 degrees.

And there's effectively no other gas in the steam, because dissolved air in the boiler's feedwater (particularly oxygen and carbon dioxide) has to be removed to prevent corrosion. To that end, water going into the boiler is first run through a deaerator, to remove any air that dissolved in the water as it came through the condensor.

Nope, water vapour is the gas phase of water mixed with other gases while steam is just the gas phase of water. Water vapour can condense into tiny droplets which can freeze into ice crystals, both of which are visible as 'clouds'. Steam is not visible until it condenses into droplets at which point it no longer is steam but water suspended in another medium, usually air.

this is an interesting distinction that i was unaware of.