You are confusing citizenship with an eligibility requirement for public office.
The USCIS recognizes exactly what you’re talking about.
http://www.uscis.gov/portal/site/uscis/menuitem.eb1d4c2a3e5b9ac89243c6a7543f6d1a/?vgnextoid=a2ec6811264a3210VgnVCM100000b92ca60aRCRD&vgnextchannel=a2ec6811264a3210VgnVCM100000b92ca60aRCRD
Natural born citizenship is not mentioned - anywhere! - on the USCIS - Citizenship page. Why? Because it is NOT a type of citizenship!
Article II, Section 1 of the U.S.Constitution makes it very clear that one need only be a citizen - native born, derived citizenship, naturalized, it doesn’t matter which - to be either a Representative in the House, or a Senator.
To be President of the United States one must meet three eligibility requirements: natural born Citizen; 35 years of age; resided the last fourteen years inside the U.S.
One must be more than just a citizen to be President. One must be a natural born Citizen.
Are you still confused?
No, it is not as simple as that. It is jus sanguinis or jus solis. Birthright citizenship is the law of the land and children born abroad to American citizen (s) can automatically acquire US citizenship. I know that as a fact professionally and personally.
There is no argument that a person born to American parents abroad is a “US citizen”, but not a Natural Born Citizen which is a “sub-set”. Our Founders intended NBC for a reason.