Yes, I've heard of Mac Mini. It's a lunchbox with a computer in it. Its size relative to regular desktop computers that could hold 20 Mac Minis, is what makes it "mini". But this is a 7.85" iPad. If that's "Mini" next to a 9.7" one, then the iMac 21.5" is an iMac Mini, or possibly iMac Nano, the MBP 13" is MacBook Pro Mini, and let's not forget the MacBook Air Mini 11".
There was also the iPod mini, 2004-2005, that was smaller than the "classic" iPod at the time, http://en.wikipedia.org/wiki/IPod. The iPod mini was effectively replaced by the significantly smaller and flash-based iPod nano in September 2005.
Thus I will not be surprised if they call the 7.85" iPad "iPad mini".