I'm of the opinion that they've always been separate entities.
But that's been disagreed for various whatever reasons. For those that disagree with the above:
They became separate entities when a Snow became King in the North.
Jon Snow at the end of Season 6 makes it very clear that Sansa is the Lady of Winterfell. Jon never took up the Lordship of Winterfell.
This is visible both here in the script, and on the following clip on youtube.
JON SNOW: I’m having the lord’s chamber prepared for you.
SANSA: Mother and Father’s room? You should take it.
JON SNOW: I’m not a Stark.
SANSA: You are to me.
JON SNOW: You’re the Lady of Winterfell. You deserve it. We’re standing here because of you. The battle was lost until the Knights of the Vale rode in.
Updates with the new episode,
When Arya arrives at wintefell she asks for Jon Snow. When the guards say he's thousands of miles away, she asks who's in charge. The guards say "The Lady of Winterfell is, Lady Stark". This further confirms the above points.
Some quibbles that have come up while discussing this with Skooba.
Sansa did not consider herself Lady of Winterfell.
This is incorrect. In the video above Sansa says Jon should have the lord room. She never objects to being the Lady of Winterfell, if she ever had, she accepted it pretty quick.
Only when Jon leaves does she have any say... any REAL say
Jon puts her in charge. He specifically says "you're in command now" That doesn't mean she's in charge of Winterfell now. What good would that do? Especially when the King and the Hand are gone. He's clearly giving her control of the North. Stand-in King of the North if you will.
The other Lords seem to think they have a say
She never had no say, she respects her half-brother, she's questioned his decision but accepted that he's in charge. In fact, no Lords really had any other say, all of them have no say, at most they question him, but as it was in the most recent episode, the decision is his, an no one else's.
Jon had the kiddie lords swear fealty to House Stark
He did, as that's his family. Swearing fealty to House Stark not only provides the benefit to his sister, the Lady. But also ensures they're in line with his family and allegiances.
You dont get to "choose" to be KitN. The Boltons could do what they did because the Stark line was expected to be extinct, notice how they moved to Winterfell once they took power.
You most definitely could not "choose" to be King in the North. That was something you had to be elected to become. Jon Snow was elected and so was Robb. They both had to be accepted by their Lords (and/or Ladies) to become King in the North.
Impressed with his leadership, the Northern houses have proclaimed him their King.
Official HBO GoT viewers guide - Jon Snow
