Hardcore - Douchebags who think they're awesome because gear.
Casual - Douchebags who think they're awesome because they don't want gear.

^ The petty arguments you're bound to run into. People who consider themselves hardcore will clown casuals, and vice versa, for seemingly no reason.

People consider me a hardcore player. I often get mocked because I always join casual guilds (or FC in this instance) despite the fact it would be better to join fellow hardcore players.

In my eyes, casual players are people playing the game for fun. They enjoy the scenery, the voices, the mechanics, the story and just the experience in general. They'll log off if something they're doing is bored. Hardcore players, on the other hand, don't play for fun. I'll farm dungeons repeatedly for something despite the fact it's boring because I get enjoyment and satisfaction from progression.

A good example a friend of mine told me was:

Casual - Will play Angry Birds when they feel like it.
Hardcore - Will start playing Angry Birds and go out of their way to reach the end, despite the fact they're bored.

Completion is a huge part of a hardcore gamers enjoyment. They go out of their way to be as efficient as possible, whereas many of my FC members have no cares if they cap their Myth tombs each week which boggles my mind while it boggles their mind that I'm willing to spend 4-5 hours doing the same content over and over to cap it.

At the end of the day you won't find a clear definition, though. The best thing to do is to come up with your own definition. For example, where do you draw the line for someone who plays a sport for a hobby and someone who players it seriously? It's a similar situation.