Steam is water raised to the critical temperature for a given pressure, and is a gas. At atmospheric pressure of 29.97 inHg with an open container, it immediately will fall back below the critical temperature and return to hot water vapor, which is not a gas.
Evaporated water (water vapor) is water in the air represented by a value we call humidity, and is not a gas, but an actual water mass whose amount or capacity is allowed primarily by temperature of the air mass.
Vapor by definition is gas, therefore it is steam, the vapor phase of water.
No, vapor by definition is a substance suspended in the air, such as a liquid or solid. Water vapor is the "gaseous" form of water, but it's not steam. Steam has a very narrow definition. It's the vapor produced when water reaches the boiling point, but it is the gas phase of water.
While you are correct in stating that steam and water vapor are both vapor, you're not producing steam with a cup of water in your car. You're just evaporating it.
Never argue with an idiot, they'll drag you down and beat you with experience.
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