* Gunsen (軍扇 troop+fan) were folding fans used by the average warriors to cool themselves off. They were made of bronze, brass or a similar metal for the inner spokes, and often used iron for the outer spokes, making them lightweight but strong. Warriors would hang their fans from a variety of places, most typically from the belt or the breastplate, though the latter often impeded the use of a sword or a bow.
* Saihai (采配 baton+distribute) were tasseled signalling fans which would be used by a commander to signal troop movements.
* Tessen (鉄扇 iron+fan) were folding fans with outer spokes made of iron which were designed to look like normal, harmless folding fans or solid clubs shaped to look like a closed fan. Samurai could take these to places where swords or other overt weapons were not allowed, and some swordsmanship schools included training in the use of the tessen as a weapon. The tessen was also used for fending off arrows and darts, as a throwing weapon, and as an aid in swimming.
* Uchiwa (団扇 group+fan) were large iron fans, sometimes built on a wooden core, which were carried by high-ranking officers. They were used to ward off arrows, as a sunshade, and to signal to troops.
I also found a video of some fan-jitsu in action.
Now you know not to trust anybody with a fan.