The thing is that steam is an invisible gas. In and around the heat of the stove, as heathfield says, it remains as a gas so you can't see it. In cooler conditions it condenses into tiny droplets of water, a visible mist.
We were always taught at school to look closely at the vapour coming out of the spout of a kettle. The first half-inch or so was true steam and therefore not visible.
My Chambers Dictionary confuses the issue by defining steam both as the gas and as the water droplets. Can't say I agree. That would mean that the fine spray of water droplets coming from, say, spraying bottle should be called steam.