Relationship between vapour pressure and saturated vapour pressure
If you're at equilibrium, you're saturated.   If you're saturated, you're at equilibrium.  The end.

If things aren't at equilibrium, the situation is different.  Consider a dish of water in the middle of the Sahara desert.  The amount of water in the atomsphere in the Sahara desert is generally nonzero, say in the range of 1 $\mathrm g~{kg}^{-1}$.  Even though the water vapor pressure (even in the Sahara!) is nonzero, it is way less than "saturated".  Therefore it isn't at equilibrium, and the pan of water quickly evaporates.