Lil Wayne, VGC is the stuff sponsored by Nintendo, and can only be played on DSs. Its the stuff with Regionals, Nationals, etc, and has prize support. Unfortunately, its a very terrible format that allows broken Pokemon to roam free (like Excadrill, Garchomp, Blaziken and Thundurus).
VG is competitively playing on a simulator, like Pokemon Online. Its usually ran by an elite group with the most amount of knowledge (the dudes at Smogon). The goal is to create a balanced environment. The result of that is a metagame/format that is much easier for new players to get into. Its also the classic 6vs6 format the handhelds games use for multi-player play, while the VGCs use Bring 6, pick 4 style present in the console games.