The difference of supersaturated temperature and saturation temperature at that pressure is called

Let's break down the terms:
Saturation Temperature: This is the temperature at which a substance changes phase (e.g., water to steam) at a given pressure.
Supersaturated Temperature: This refers to the actual temperature of the vapor when it is cooled quickly and condensation doesn't happen immediately. It's in a state where it should be condensing, but it hasn't yet.
The difference between these two temperatures is a measure of how much the vapor is "held back" from condensing.
Option A: Degree of super-saturation is the correct answer, since it describes the situation of vapor holding more vapor than in saturated condition.
Option B: Degree of superheat refers to how much a vapor is heated *above* its saturation temperature, which is opposite to what the question describes.
Option C: Degree of under-cooling refers to the temperature difference when a liquid is cooled below its freezing point without solidifying which is irrelevent here.
Therefore, the correct answer is A: Degree of super-saturation