Yeah, but unless you have a Japanese 3DS, good luck playing that version. I'm sure anyone would know they mean MH4U. If you wanna be nitpicky about things, you should also point out they referred to Monster Hunter Tri as Monster Hunter 3. :^)
I'm not nitpicky, MH4 and MH4U are two completely different games.
MH3 and MH tri are basically the same thing, just people call them by different titles. And on the same topic, I can understand people calling Majora's Mask 3DS just Majora's Mask, without the 3DS suffix, because there
is a game called Majora's Mask on the 3DS, and there is a game called MH3/MH tri, it's just how you prefer to pronounce it. The problem with calling MH4U "MhH4" is, unlike how MM3DS/MM and Mh3/MH tri are the same game, no matter what you call then, there's no two different games for both titles - unlike with Monster Hunter 4, and Monster Hunter 4 Ultimate, there
is a game on the 3DS called Monster Hunter 4, and there is one called Monster Hunter 4 Ultimate. If there was no game called Monster Hunter 4, then yes, valid point, but the problem is that there is a game called Monster Hunter 4, so referring to Monster Hunter 4 Ultimate as Monster Hunter 4 is referring to a totally different game.
MH4 is a game that only got released in Japan. MH4U is the game that got released in the west, and a localized version of the Japanese "sequel" to MH4, called Monster Hunter 4G. There is no game called "Monster Hunter 4" released in the west without a Japanese import - it's an entirely different game to Monster Hunter 4 Ultimate. Monster Hunter 4 has less monsters, less areas, no G rank (which is a
huge part of the game), no Dondruma Town, no 4th gen monster subspecies, heck even some of the weapon controls are completely different in MH4 than they are in MH4U/G. It's got similar features to MH4U, but they're not the same.
Calling MH4U "MH4" is like calling Pokemon Emerald "Pokemon Ruby/Sapphire", or X and Y "Omega Ruby/Alpha Sapphire" - they're completely different games, just because they're similar doesn't mean they're the same or that I shouldn't "nitpick" because they are referring to a completely different game in the series.