Wi-Fi, WiMAX, TVWS are all a kind of network standard used for data communication. Wi-Fi relates to IEEE 802.11; WiMAX relates to IEEE 802.16; TVWS relates to IEEE 802.22. Depends on the need / use-case, mix and match of these standards could be used. In many cases, ISP help is required for connecting to outside world of internet.
Wi-Fi is a common term nowadays (technology allows electronic devices to exchange data wirelessly). We use at home for streaming videos / audios from our media collection / internet sites wirelessly.
WiMAX is similar but uses mobile technology like http://en.wikipedia.org/wiki/Clearwire.
TVWS (TV White Space) has its own line of benefits as mentioned in the following web pages. Mainly used for low cost long range transmission using UHF spectrum.
Use-case implementation of TVWS is promising depends on how you view it (< 3 Mbps speed is very good for developing / under-developed countries and education institutions for using internet). Power of internet is self explanatory.
- Wi-Fi hotspot extends Clearwire’s WiMax service (reviews.cnet.com)
- White spaces networks are not “super” nor even Wi-Fi (gigaom.com)
- Urban Legend of Free Wi-Fi For the Masses: Devil In The Details (mayo615.com)
- Idea launches Wi-Fi services in 5 Indian cities (trak.in)