From Diablo Wiki
D3C = Diablo 3 Classic. D3V = Diablo 3 Vanilla.
Both acronyms refer to the basic version of the game, though this is a moving target with numerous major content patches responsible for major changes to the game over 2012 and 2013.
The terminology is a common one for video games that have seen one or more expansion packs. Diablo 2 is often referred to as D2C and the expansion pack is dubbed D2X. Diablo 2 was not commonly called "Diablo 2 Vanilla" though the initial release of World of Warcraft is often known as "WoW vanilla" to refer to the basic, plain version of the game.