Alright. I'll chime in among all the attacks and give my honest opinion on what may be the difference between a "gamer," and a "true gamer." Like I said this is all opinion, so if you say I'm "wrong" in my opinion, you have no idea what an opinion is.
Gamer- The guy who buys every iteration of Call of Duty and Halo every year....and mostly nothing else. They play online with their buddies every night and have a good time. Hooray for them.
True Gamer- Person who has perhaps grown up playing games and has a strong appreciation for them, whether it be for the stories, intense action, fun, moving moments, etc... They also have an appreciation for both single player AND multiplayer aspects, yet can still have a preference among the two. Also usually doens't like to see either aspect HELD BACK because of the other. True gamers are also usually prone to supporting new IP's and ideas in video games, and are looking for video games to grow, rather than be stuck in a repetetive cycle where the same game is released every year under a new title (yes, I'm taking a jab at COD.)
I'm pretty sure everyone on this board are true gamers, as I do often see people speek passionatly about what they like and don't like. Most attacks of "you're not a true gamer" I've seen on this forum are absolute bull. Quit being a bunch of babies. You're all true gamers... unless you keep attacking each other. Then you're just weiners.