Gamer. Someone who spends money to play games. Not someone who only spends money on free to play games in order to get further by playing the game less. So this includes people who spend a bunch of money in Minion Madness, or Jetpack Joyride, or Farmville, but not people who play those games and spend maybe $10-20 dollars.
Hardcore Gamer. Someone who goes looking for games to buy regularly. Example if I say Humble Bundle, and you go to that website, and then hit up GoG for sales, and then steam sales, you're a hardcore gamer.
Casual gamer. Someone who will play Hohokum, Journey, or a few other games that don't require reflexes with a handful of games that do.
True gamer. Someone who takes a break from hardcore gaming sessions by throwing in some Flower, Minecraft, Hohokum, Jouney, and other pallete cleansing casual titles.
Fake gamer. Someone who says "Omg really? More indie games?"
Ungamer. Someone who buys Call of Duty, Destiny, Madden, GTA, maybe a racing game, and what ever other game everyone talks about. These are the people that ONLY play what sells in the millions to 10s of millions ranges. They don't even really care what else is out there. Unless everyone else is playing it, they don't want to.