GP and GGP are describing different methods of cooling:

Sitting in a breeze does two things: 1) Allows your sweat to evaporate more quickly, and that evaporation is what causes most of the cooling effect. It's not very effective in high humidity because your sweat won't evaporate very easily. Evaporative coolers / swamp coolers work off this same principle. 2) Sitting in the still indoor air your body heat warms the air around yourself and you end up sitting in that pocket of heat. Just about any airflow stops that, which is why air circulators (fans that are meant to point from one end of a room to another instead of directly on a person) work to make a room feel a bit cooler.

Running the attic fan at night with open windows can have similar effects as above (especially the air circulator), but on top of that it's for pulling in the air from outdoors after it's cooled off at night, and expelling the warmed-up air that accumulates near the ceilings and roof. You'd want to close windows in the morning so the warmed-up air doesn't get pulled in and replace all the cooler air.

Fans don't improve comfort as much if humidity is high, because the airflow doesn't cause as much evaporative cooling on the skin. So you need a temperature gradient to get a good effect. Attic fans are a good example. The attic tends to get hotter than the outside air when the sun is shining, and the fan helps equalize.