Hard core gamer is just another term for what we actually are: video game enthusiasts. I.E. someone who considers gaming to be a way of life. They are versed in the industry, they know about its history, and they spend most of their time either thinking about, or actually gaming.
It's sort of like with cars. There are people who buy a car, drive it until it doesn't work and then buy another one. Then there are gear-heads, which is the car-equivalent term for car enthusiasts.
Is it a way of life? Then you're a core gamer. Is it something on your phone that you screw around with every now and then? Then you're casual. And so forth.