Both these terms are very common these days, as Wireless technology is getting wider and wider everyday, Every new laptop, Pocket PC and most models of cellular phones has capability to receive wireless network signals. However Wi-Fi and Wi-Max are different.
WiMAX is a technology more employed by Telecoms Operators to serve Internet connectivity, wirelessly throughout a region or large area. Wi-max signals cannot be picked via the regular Wi-Fi card used in laptops or pc or a cellular phone.
Wi-Fi, as seen and used in the home or office, is similar in that it connects through the air, but the range is much lower and it is predominantly used in the home and office.