There's no appreciable difference at all between the core reasoning and the final declaration.
If someone is a natural born citizen, then they're a citizen.
Your utter determination to deny what they law says is showing.
Let me reword that, as that might be, in one sense, overstating the point a bit.
The case asked the question of whether Wong was a citizen.
The Court examined the question at length, and quite clearly found that he was a natural born citizen.
So in the final declaration, because the question before the Court was, "Is Wong a citizen?" they answered, "Yes, Wong is a citizen."
But the entire core reasoning of the case was that he was a NATURAL BORN CITIZEN.
Since the entire core reasoning of the case determined that he was a NATURAL BORN CITIZEN, and that core reasoning was... well, THE CORE REASONING, completely and absolutely central to the outcome of the case, then that CORE REASONING - and its CONCLUSION, that anyone in Wong's situation is a natural born citizen, is absolutely binding precedent.
I hope that's stated a bit better.