I like the distinction between 'core' and 'casual', but it's probably the marketer in me. Market segmentation is a huge part of the marketing process - you have to know who is interested in your product, how many of them there are, where they are, how to contact them, and how to talk to them.
So I think, on the marketing side of the gaming industry, I bet 'core' and 'casual' categories mean a lot more than they do to gamers tossing the terms around on message boards.
For gamers, I think core gamers fancy themselves the taste-makers of the industry. They're the ones that are clued in about what games are good or not, and they're the centers of influence from which their more 'casual' gaming friends pick up recommendations, or see something cool.
CoD started off as a core franchise. It was core gamers that bought CoD4, played the shit out of it, and it was through them, over time, that a larger more mainstream audience that maybe buys one game a year decided 'hey, that's cool, I want to play that too'.
Core gamers can be fans of any genre, can put as much time in any number of games as they want. It's the knowledge and the passion for the games they love that seperate them from casual gamers, who could go on living quite happily if they were banned from ever playing a videogame again.