Wireless Technology basically does the same thing as the technology would do, except for the fact that it is done without wires. For example Spectralink Wireless Products are just normal telephones that operate wirelessly, so that you can bring the phone with you.
Wi-Fi is often used in replacement for the word "wireless" and it simply refers to certified products that belong to a class of wireless local area network (WLAN) devices based on IEEE 802.11
According to Wikipedia Wireless is:
"Wireless communication is the transfer of information over a distance without the use of electrical conductors or "wires". The distances involved may be short (a few meters as in television remote control) or long (thousands or millions of kilometers for radio communications). When the context is clear, the term is often shortened to "wireless". Wireless communication is generally considered to be a branch of telecommunications."