For semantic reasons I think we all know that in these arguments when these terms are used it generally under these definitions:
Casual - Player of fringe/low level play ability. Plays mostly "casual" titles like Angry Birds, Candy Crush, Tetris, maybe venturing out as far as say Mario Kart as their most complex gaming experience. Likes games but isn't obsessed with them, doesn't follow the industry, don't really care about "beating" a game, like to get the high score though. Games are a fun little time burner, not something to be taken seriously. Low level skill, don't like games that are too complex or confusing, generally don't like hyper violent games either (Candy Crush not Grand Theft Auto). Drove the Wii Sports/Fit/Kinect crazes for a while before moving on to smart devices.
Hardcore - Generally speaking males aged 11-35 year old though there are women who also make up this group. Like to play games with more advanced play mechanics than smartphone/mini-game titles. Generally favor these genres -- shooters, action games, 3D platformers, racers, sports games, RPGs etc. Can also enjoy simpler games but prefer the deeper/more complex games, enjoy features like online play and competition. Knowledge of industry can range but they generally know things like Mario is only on Nintendo systems, a Playstation is not an XBox, Calladooty every November, all the way up to religiously following events like E3, etc. etc.
Nintendo Hardcore - Subset of the general hardcore gamer, except they love Nintendo franchises and are active in buying Nintendo product now (not as in "I loved Zelda on the Super NES" type thing). Not just Mario (as a casual gamer would), but some combination of Metroid and Zelda and Pokemon and Smash Brothers etc. The more hardcore even go for F-Zero, Pilotwings, Wave Race, Mother/Earthbound, etc. This group has been shrinking since the 90s, but remains staunchly loyal to Nintendo (well Mario and Zelda and Pokemon at least).