I don't agree with any of those lists. To me a core player is one who can't be traded because his value and leadership is too high to the team. Sutter and Lombardi go to these players to get the most important jobs done on and off the ice.
It's not a list of the best prospects the Kings have developed into good young players, plus Richards and Carter.
Core:
Williams
Scuderi
Mitchell
Brown
Doughty
Quick
Stoll
These players are the playoff leaders who either have led us and led others to the promised land
Next tier, still core:
Kopitar (he will need to be better at faceoffs, our defensive leader)
Richards (winner and leader everywhere else)
Carter (now our leading goal scorer this year, last year not bad)
Greene (sorely missed...better than Regher)
All of these guys are almost there.
Next, next tier:
Lewis
Clifford
Voynov (he's about to move up though still no where near Doughty)
These guys are top tier role players.
Not present:
Fraser
Martinez
He should be close to core but didn't show it this year.
Not sure:
Penner (UFA status)
Toffoli (still young, high hopes)
Not core:
Nolan
King
Bernier (about to be traded)