“Casual” being the obvious first step. These are people who occasionally pick up a game. Maybe it’s the simple round of Tetris or maybe spend some time with their Sims family. Maybe it’s tending their farm in Farmville or some other various game on Facebook or phone. This person might have a Kinect, PS Move, or a Wii and enjoys the silly fitness games. Either way, it’s casual.
“Social” is someone who mainly plays games with friends or just online. This is a bit similar to Casual gamers but the difference is the actual games. Sports games, CoD, Gears of War, etc. These are the kinds of gamers who never actually do anything to get into tournaments or competitions, but have some form of fun with it.
“Core” is the kind of person who plays a variety of games and does more with them. This person might be competitive or might have fun with multiplayer. This person might play single-player games like MGS or Mass Effect and enjoy the story/gameplay. This person might be a jack-of-all trades in the various genres. Nothing over-the-top but nothing below the bar.
“Hardcore” would be the top tier. They do research on how to improve their gameplay and strategies (Starcraft). They train for competitions (Street Fighter). They learn the ins and outs of a game and do more than just “play it” (Pokemon). This could pertain to a singleplayer or multiplayer game.
If there is anything anyone wants to add, remove, or change. Let me know.