Furoba said:
When they first announced (before anything was known) SSBB, they said "WiFi" though. ;p
I believe the official way Nintendo treat it is this:
WiFi = the hardware definition of WiFi, simply communicating between two devices wirelessly.
Nintendo Wi-Fi Connection = Connectivity over the internet (using WiFi, generally, although I guess that's not necessary with the wired Wii dongle)
Unfortunately, people generally don't latch onto the terms accurately, so sometimes people refer colloquially to WiFi when they mean Nintendo Wi-Fi Connection and sometimes people think you're talking Nintendo Wi-Fi Connection when you're just saying 'WiFi'.
It's a game of Telephone (Er. I think that's right. The term I want to use, I'm dimly aware is somewhat offensive outside the UK, I think that's the US name for the game I'm referring to, though)