Well first, if your only a PC gamer, your not a hardcore "Gamer" ;p Sorry PC Master race and all but your not hardcore usually without at least a decent pc, 2 currentish gen consoles and a current gen handheld.
Now on to the actual topic in retail terms, Casuals only buy a few select games, and the current versions of those games, While a core gamer buys the games of a causal gamer but generally expands on what they like due to recommendations from friends or "This game is GOTY dog." Core basically just doesn't own more niche or underwhelming like a hardcore gamer would.
Like a casual library would be : Call of Dutys, Maddens, GTAs, Mario, LoL, Last of us
Core library would look more like : Call of Dutys and battlefields, A couple sports titles, GTA and saints row, Mario and Rayman, LoL and Dota2, Last of us and Bioshock, Tomb raider, Farcry.