Ha ha ha, I take no offence, don't worry. I have no problem with being pointed out as being wrong...if it's true
In this case though I am pretty sure this a semantic terminology thing. They are still very different.
When you AirPlay an online or streaming video only, the device, whether it be an iPad, iPod, iPhone, or Mac, actually pushes the stream over to the ATV itself, meaning it takes over the stream directly. This has been verified numerous times by people having monitored their network activity.
When you AirPlay mirror (ie Display Mirroring), you are streaming over your desktop screen live over the network - so if you mirror your desktop playing a streaming video, the Mac is still streaming the video AND THEN sending the contents of the screen to the ATV.
Its almost like a double stream of data so depending on the Wifi network, can make a significant difference in performance.