The term wi-fi is not a technical term . It is expanded as as wireless fidelity , just like we use the term hi-fi to denote the high fidelity music systems .
actually wi-fi is a certification process for wireless inter-operability conducted by a consortium named wi-fi alliance for your 802.11 compatible devices .
It means not all your 802.11 wirless equipment are wi-fi certified and hence can not be officially called a wi-fi device . This kind of a certification process came in to the field because the IEEE does not test any of these wireless products to find if they meet IEEE specifications. I personally think that IEEE has a real lousy approch towards their wireless standards in general and did not even care about the security aspects of the same.
Even though the wi-fi alliance claim themselves to be non-profit consortium , they charge a hell of an amount for the certification process so not every organization will apply for the wi-fi certified status for their products .
But now the term wi-fi become an alias name for the wirless networking so do not worry about calling your non- wifi certified networking product as a wi-fi device