Nope. Wrong again, Kleon.
I keep telling you to read the Citizenship section of United States Citizenship and Immigration Services online site.
Natural born citizenship IS NOT a type of citizenship. It is only an eligibility requirement for the Presidency.
You keep making stuff up for you hero, Obama. Shame on you!
Native and natural born are interchangeable, so it fits into your list of types of citizenship. As for derived citizenship, it's just a form of naturalization, or citizenship derived after birth. This is what your link says, so I don't see where your confusion comes from.