I think it is almost impossible to define hardcore or casual games.
It is easier if you try it with the gamers. As some already said, casual gamers are just consuming while hardcores really want to finish a game.
This means that casual games are games which fit better to casual gamers and hardcore games are games which fit better to hardcore gamers. But the difference is not the genre or something like this, but the way a game is structured. Sports games are in general very casual in my opinion. When you buy such a game, everything can already be chosen and you can just pick it up and play. On the other hand, all those single player games are for hardcore gamers, because you have a goal there and all you want to do is finish it. This is very true for Mario, for Final Fantasy or for Halo. But also a game like Mario Kart is at least for both, hardcore and casual gamers, in my opinion. You can just play it if you buy it, but you can also unlock the higher classes, the mirror mode an additional characters and you have to spend a good amount of time to do that.
This being said, i think it is important for us gamers to get over this hardcore/casual question if we want that our passion really gets widely accepted. I mean, nobody speaks of hardcore movie fans or casual music listeners, do they?
