Wi-Fi vs. 802.11
Wi-Fi is a subset of the 802.11 standard that is managed by the Wi-Fi Alliance. Because the 802.11 standard is so large, and the process required to update the standard can take awhile (it's run by a committee), nearly all of the major wireless equipment manufacturers decided they needed a smaller, more nimble group dedicated to maintaining interoperability among vendors. This resulted in the creation of the Wi-Fi Alliance.
The Wi-Fi Alliance assures that all products with a Wi-Fi-certified logo work together. This way if any ambiguity in the 802.11 standard crops up, the Wi-Fi Alliance defines the "right thing" to do. It also allows vendors to implement important subsets of draft standards (standards that have not yet been ratified). The most well-known example of this is Wi-Fi Protected Access (WPA) or "draft" 802.11n equipment.