Welcome back. You've probably noticed it on a chilly morning: pour hot water into a mug, and a cloud of steam rises right away, but cold tap water just sits there.
That difference is real, and the explanation is simpler than it looks.
Water is always evaporating, even when it's cold. The molecules at the surface are constantly jiggling, and the fastest ones occasionally break free and become gas. When you heat water, you give every molecule more kinetic energy, so a much larger share of them have enough speed to escape. At 20 degrees Celsius, only a tiny fraction of surface molecules can leave. Near 100 degrees, that fraction jumps dramatically. That's why a hot cup produces visible vapor within seconds while a cold glass produces almost none.
What rises off hot water isn't actually water vapor, because true water vapor is invisible. What you're seeing is tiny liquid droplets that form when the escaping vapor hits cooler air and condenses back into liquid. This is why the visible cloud appears a few centimeters above the surface, not right at the water line. The air just above hot water is still warm enough to keep vapor invisible, but a bit higher up the temperature drops and the vapor turns into the mist you can see.
The temperature of the surrounding air matters as much as the water itself. On a cold morning, say, at 5 degrees Celsius, the temperature difference between the hot water and the air is large, so condensation forms quickly and near the surface. That's why you see thick vapor rising from a kettle outdoors in winter but barely anything in a warm kitchen. The same principle explains why your breath shows up on a cold day but not a warm one, since exhaled air carries moisture that condenses in cold conditions.
Cold water doesn't stay completely still either. A glass of tap water left out will slowly disappear over days, just much more slowly. At room temperature, evaporation in an open container occurs at a rate measured in fractions of a percent per hour. Heat speeds that up by a huge margin, which is why a puddle dries in hours on a hot day but can linger for a day in cool shade. The mechanism is identical; only the speed changes.
You can test this yourself without any equipment. Boil water in a kettle, then pour it into two identical mugs: one with hot water and one with cold. Watch both for a minute. The hot mug will show a clear plume while the cold one shows nothing. Try it again near an open window on a cool day, and the difference becomes even sharper. This same effect is why a hot shower fogs a bathroom mirror so quickly: the warm, moist air hits the cooler glass and condenses on contact.
The next time you see vapor curling off a hot drink, you'll know exactly what's happening: fast molecules escaping, then turning back into droplets the moment they hit cooler air. Try the two-mug test on your next cool morning and watch how differently they behave.