If asked to describe myself, the only answer I could truthfully give is "A Gamer". Granted, even I argue that it is the right term to describe myself, but it's definitely the best fit.
I don't claim to be a hardcore gamer. Perhaps a heavy gamer, but not hardcore. The distinction is often a little fuzzy, but I view it in terms of intent. I play, because I enjoy playing. I don't play to be the best, because I know I never will be, and I don't play the same game constantly - I like to play a variety of games, and enjoy myself doing it.
These days I'm a much bigger player on XBox Live, mainly working on co-op games. I've done a lot to help friends through Gears, Borderlands, GTA, and more. I've also started to actually use the PS3, loving God of War just now, and intending to move onto Infamous next, along with a huge list of other games.