A wireless LAN is one in which a mobile user can connect to a local area network (LAN) through a wireless (radio) connection. A standard, IEEE 802.11, specifies the technologies for wireless LANs. The standard includes an encryption method, the Wired Equivalent Privacy algorithm. High-bandwidth allocation for wireless will make possible a relatively low-cost wiring of classrooms in the United States. A similar frequency allocation has been made in Europe. Hospitals and businesses are also expected to install wireless LAN systems where existing LANs are not already in place. Using technology from the Symbionics Networks, Ltd., a wireless LAN adapter can be made to fit on a Personal Computer Memory Card Industry Association (PCMCIA) card for a laptop or notebook computer.
Definition provided by Whatis.com.

Wireless WAN:
A WAN or wide area network is a data communications network that covers a large geographic distance such as an area of 100 miles or more. A wireless WAN is a network that uses a medium that is dispersed through signals in a form of a radiowave or beams of light. As you have already guessed, the other method of data communications is through wires. Why Wireless?
Wires sometimes can hinder expansion of data communication networks because it may cost a company a large amount of money to lay wire in a certain area. Also, wires have a smaller distance of carrying the signal before it has to be amplified or repeated. Sometimes distance creates a problem for a company because it is not close enough to a central office or does not have fiber-optic cabling in its building. In other cases, buildings are not capable of importing cabling within its walls, so the only other solution is for a wireless network.

A wireless WAN creates solutions for all these situations. When data is sent using radiowaves, distance is not a huge problem. The cost of implementing a wireless WAN would be less compared a traditional wired-network.
Definition provided by Texas Tech University.