We should just call this the rain page. Nature has a few different variations of Natural Distillation. Rain is the most obvious. It is the end result of evaporation, condensation and finally rain.
Lesser ways of this process would include:
2) Scotch mist (this is actually a variation of rain with the right atmospheric conditioning)
3) Hail (Frozen rain droplets built up in layers)
4) Snow (More frozen rain)
5) Frost (Direct condensation from a gas to a solid (moisture in the air freezes out (dew point)))
6) Dew (Moisture condenses right out of the air onto surrounding objects (dew point))
The key here is condensing water, be it from a cloud or when the temperature drops lowering the dew point of the air. Warmer air holds more moisture. When the temperature drops, the atmosphere can no longer hold that much water and it drops out or precipitates onto anything and everything around.
I have included some related terms for "Distillation".