Few comments:

I think it's easier for a female to say she's a "gamer" than a guy to. When a guy says it, they are interrogated how much they actually play and what not. But if girl says, "Yeah I play Halo on Live". Then people tend to think, "Oh wow she is a gamer!" Without asking her how much she plays or what rank or blah blah all that. That's how it seems to me.

Secondly, people always classify it into, casual gamers, and hardcore gamers. I think the middle "Gamer" is well what should be middle ground. When I think Casual gamers I think the person who got a wii and plays mariocart occasionally. I think of a gamer as someone who plays games and beats them but they wont obsess like crazy. A hardcore gamer is someone who gets every achievement for every game and spends most their time working on said achievements.

That's my opinion on casual vs hardcore :P