A gaseous substance will be called a gas if it is above its boiling point, but a vapor if it is below. This sounds precise enough, but actually it is not. There is a lot of confusion to be sorted out.
If you leave a shallow container of water in the open air, it will soon dry up. It has evaporated, which means that the water has turned into a gaseous state while never exceeding a temperature of, say, 30°C, far from its boiling point of 100°C. If it had turned into a gaseous state the proper way, by heating and bringing it to its boiling point, there would be no confusion about what we should call it. Definitely, a gas. But that which exists in the atmosphere, by all intents and purposes gaseous, filling all the criteria of a gas, is not given the distinction. Instead it is called a vapor.
Now, what happens to the water that comes through the proper channels? It reaches 100°C or above, turns into a gas - a proper gas, "water gas" - and disappears into the atmosphere. Of course, once in the atmosphere, it cannot maintain such high temperatures, and therefore cools down to the ambient temperature. In doing so, comes way below the boiling point, and might even reach near zero temperatures without turning back into water again. In fact, evaporated water and boiled water, both come together to form what we know as atmospheric water vapor. The distinction made in the opening sentence of the article has vanished altogether.
Neither is it true that water vapor does not turn back into water. It does so all the time. It is the mechanism by which fog form. But there is no hard and fast rule for this. When the humidity of the air rises to a sufficient level, condensation may be triggered by various meteorological factors. Most commonly, condensation is triggered by the presence of dust particles in the air, giving rise to clouds, which eventually become too massive to sustain themselves, and results in rain. There is no particular temperature in which this occurs.
So you need to ask yourself, why are the rules of temperature (freezing point) flouted so regularly? It must be pointed out that it is not only water, but all substances behave in the same way. Thus, if the substance is supposed to be liquid at a certain temperature, and has a free surface, evaporation is always taking place, giving rise to a vapor of the substance, which is essentially a gas. Even solid states are found above the freezing point, and liquid states below it (illustrated by phase diagrams).
Boiling point and freezing point are not meaningless concepts either. In controlled laboratory conditions, a substance displays well-defined transitions of state when going through these points. In order to understand how the exceptions come about, specifically regarding the distinction between a gas and a vapor, the kinetic theory of gases helps.
This theory imagines the molecules in a certain volume of gas to be moving randomly in all directions and with all speeds. But the speeds may be averaged, and this gives a measure of the temperature. To heat the gas is to impart to the molecules greater speeds, giving rise to an increase in temperature. On the other hand, the molecules hitting the container wall exert pressure on it, which will also be averaged out across a certain area. This is nothing but the pressure of the gas at that certain volume and temperature.
Now, the beauty of the kinetic theory of gases is in the process of averaging things out. If we do so, we get the elegant explanations of temperature, pressure, volume, and the mutual relationships between all these, known as the ideal gas laws. But it cannot be taken too strictly either. Certain molecules may be very slow, and if such a molecule approaches another slowcoach, the two condense out of the gas and become liquid. A few dust particles hanging in the gas will help the process along.
The opposite process can be imagined taking place in a liquid. The kinetic model may also be applied to a liquid, only with further reservations regarding the freedom of the molecules. Certain liquid molecules acquire such speeds (the speeds being distributed randomly; the normal distribution) that some of them may escape the liquid and become gaseous. Increasing temperature will help this process.
So when boiling water, it doesn’t need to reach the boiling point to acquire the gaseous state. Evaporation is always happening, and continues to increase with temperature. In fact, the vapor that emerges from the liquid may be thought of in terms of pressure. It is the pressure of all the emerging gaseous molecules that exit the open surface of the liquid. This is called vapor pressure. In fact, the boiling point is defined as being nothing other than the temperature at which the vapor pressure equals atmospheric pressure (Raoult’s law). In other words, the molecules of the liquid have all been excited to a level equal to the molecules in the atmosphere, and therefore the liquid cannot help becoming gaseous as a whole.
Seen in the light of the kinetic theory, there is a continuum between a liquid and gas, and they are not really separated by a definitive boiling point. The boiling point, of course, has significance related to vapor pressure, as seen above. But there will always be a shifting equilibrium between the two. What is observed in a cloud is the condensed droplets, which are in a state of equilibrium with the invisible vapor. The same applies to steam. But it is not a bad convention to call a gas a vapor below its boiling point, and a proper gas about it. The existence of clouds and steam point to the underlying presence of vapor.