Like Roy, KIng does some things he learned from Dean and some of just his on ideas. That is what you look for in a head coach, taking what they have leaned and building on it to fit in to today's game. How the game was played 60yrs ago is very different from the way it is played today so any system, even the Carolina way has to adapt to the current reality. Like our constitution, it is an ever evolving thing yet still hold immutable truths that should never change.
I think what you are more asking is does King follow a similar approach to the offensive and defensive sides of the ball rather than the Carolina Way. For example, the Carolina Way is not that UNC fast breaks as much as they can, that is an approach or you can call it a skeme, maybe even system. The Carolina way is more about what defines UNC like "play hard, play smart, play together", like UNC is family, we were family before family got cool, now everyone wants to think they are family. The Carolina way is NBA players coming up to that UNC rookie and letting him know, we family, what ever you need . It is things like Dean always being there for every one of his former players, from walk ons to MJ, a walk on looking for a job and Dean would makes calls even thou it had been 20yrs since that guy played for Dean.
The Carolina Way is like in a business proposal your first step is to set in stone your mission statement, the Carolina Way is the UNC mission statement, everything else is about how you achieve that mission.
There is a lot of discussion now about some of our former players saying some things publicly that Cadeau's family don't like. Some times the best thing family can give you is tough love, what you really need is not always what you want to hear and what Theo, Raymond, and Justin had to say was maybe not what Cadeau's family wanted to hear but it was exactly what Elliot needed to hear even if he is not yet mature enough to realize it.