Hardcore Gamer = A person who plays games for the challenge. They play games as a serious hobby, not just for pick up & play fun.
Casual gamer = A person who plays games just for fun. They don't take it too seriously & uses it just like they would a movie. It's just entertainment
Mature Game = A game that's not family friendly. Can a little girl watch you play it? Would you feel comfortable playing the game in front of that little girl? No? It's a mature game
Non-mature game = A game that anyone can watch / play without feeling uncomfortable in any way
My view