I think the "HD Twins" thing started because the Wii was clearly not in the same graphical league as the Xbox 360 and PS3. It was a way to differentiate between HD games that could not run on the Wii unless gimped.
From my perspective, it started as a veiled insult towards the consoles from Nintendo fans. Really the same thing with PS360, to represent and gently mock the fact that the two consoles were trying so hard to be so similar to one another
Monster Hunter: pissing me off since 2010.