Hey thanks for clearing the two terms in such precise and easy way punching_bag69!!
But let me clear out that Wi-Max is not a wired data transmission system.
There is not much difference between the two.
WiMAX is a wireless digital communications system, that is intended for wireless "metropolitan area networks". WiMAX can provide broadband wireless access (BWA) up to 30 miles (50 km) for fixed stations, and 3 - 10 miles (5 - 15 km) for mobile stations. In contrast, the WiFi wireless local area network standard is limited in most cases to only 100 - 300 feet (30 - 100m).
WiMAX can be used for wireless networking in much the same way as the more common WiFi protocol. WiMAX is a second-generation protocol that allows for more efficient bandwidth use, interference avoidance, and is intended to allow higher data rates over longer distances!
I hope this clears the point...
