The difference is simply natural born vs. native born. A person can be either and not the other. Natural born is of two citizen parents, native born is on US soil. Funny how the OBOTS throw these around like they are interchangeable....they are not!
The confusion is the result of the fact that in the past the terms were used interchangeably. It is only with serious scrutiny that you can distinguish a difference in the meaning between "natural born" and "native born" in the 18th and 19th centuries. The terms WERE used interchangeably, because the overlap between the two was nearly 100% in those days. As I am fond of pointing out, the Chief Justice of the Supreme court in 1874 said:
"...all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives or natural-born citizens, as distinguished from aliens or foreigners. "
Nowadays, because we have so much illegal immigration and travel, we do note a great distinction between the two terms, but I do not believe that was the practice a hundred years ago. It was simply easier to say "native" than it was to say "natural born citizen", so laziness contributed to the somewhat inaccurate use of the former. Besides, in 99.999% of the cases, the term "native" works just fine. The distinction between it and "natural born citizen" only matters when the issue of the Presidency is being discussed.