Possibly due to the fact both WiMAX and Wi-Fi are based upon IEEE standards beginning with 802. and both have a connection to wireless connection technology, comparisons between the two are frequent. Despite this, both standards are aimed at different applications.
WiMAX is a long range system, covering many kilometers, that uses licensed or unlicensed spectrum to deliver a point-to-point connection to the Internet from an ISP to an end user. Different 802.16 standards provide different types of access, from mobile (analogous to access via a cellphone) to fixed (an alternative to wired access, where the end user’s wireless termination point is fixed in location.)
Wi-Fi is a shorter range system, typically hundreds of meters, that uses unlicensed spectrum to provide access to a network, typically covering only the network operator’s own property. Typically Wi-Fi is used by an end user to access their own network, which may or may not be connected to the Internet. If WiMAX provides services analogous to a cellphone, Wi-Fi is more analogous to a cordless phone.