I prefer the term "gamer" at it's most literal: a person who plays games. Crysis, Halo, Uncharted, Mario, even chess; if it's a game, and you play it, you're a gamer.
"Hardcore" and "casual," on that other hand, I only ever use to denote a game's intensity level. The more you have to focus to progress in the game, the more "hardcore" it is.
I do NOT use the terms to discriminate against games, hardware, or other players. Arguing over video games with unintelligent slugs who can't see past their own pimples is a waste of time and energy.