Anybody who "games" is a gamer. You can divide the community in whichever segments you like.. but I think there is 2.. no more than 3 groups.
Casual: They'll play a game from time to time, maybe once or twice a week. They probably own one console and it's probably a PS2 with no more than half of the games completed. If they have a PC, it's not likely equipped well. Most people I know are casual gamers. They could probably name only the most well-known game developers (Nintendo, Sega, Sony, Microsoft, EA, Rockstar) ... They may play online if only because the option is there.
Hardcore: Most people that'd post here have been hardcore gamers at one time or another. Basically, these people are the ones that care enough to
discuss games. They incontrovertably have more than one gaming platform in their home. Not every hardcore gamer has a mid-high end PC, but those who specialize in PC gaming usually do. Gaming is an artform to them that demands respect, where as to casual gamers it's a fun time-waster. They can probably name a bunch of game developers. (Hideo Kojima) They play online and can be very competitive but do it mostly for pure fun.
Before I go on to the next group.. I should say that IMO if you have a friend that plays only one game..
No matter how many hours they play it.. they're definitely casual.
If there is a third category, I'd consider it a transcendent version of the hardcore gamer. Let's just call it,
Pro: These people are intense. If you've ever seen one of those "game room" guys with 5,000 games and 10+ consoles.. that's "pro". If you see somebody craft a case that looks like the Doom 3 space station, that's what I'm talking about. If you have a weekend warrior, living-in-his-parents'-basement nerd that spends virtually all of his income on games and beats the majority of them and masters others.. that's a pro. Now, you might think me something of a fool to confuse true "pro" gamers like Fatal1ty with uber-nerds.
I consider a guy that spends upwards of $10,000 on games just as focused on the lifestyle as I do a guy that plays upwards of 6 hours a day of a single game for a year so he can play in CPL matches and win more money in a year than some of you will make in the next decade.
The only difference is.. one person plays 50 different games a year.. one person plays 1-2 and rips the living shit out of his opponents.