Your categories one and two have been considered the same category since the late 19th century. Since the adoption of the Citizenship Clause of the 14th Amendment in 1868, no law passed by Congress and no court decision has ever separated natural born citizens from citizens of the United States at birth.
Two recent examples of court rulings on the issue:
Tisdale v Obama, US District Court Judge John A. Gibney, Jr.: “It is well settled that those born within the United States are natural born citizens.”— Tisdale v Obama, US District Court of the Eastern District of Virginia, January 23, 2012.
http://www.scribd.com/doc/82011399/Tisdale-v-Obama-EDVA-3-12-cv-00036-Doc-2-ORDER-23-Jan-2012
Voeltz v Obama, Judge John C. Cooper, Leon County, Florida Circuit Court Judge: “In addition, to the extent that the complaint alleges that President Obama is not a “natural born citizen” even though born in the United States, the Court is in agreement with other courts that have considered this issue, namely, that persons born within the borders of the United States are “natural born citizens” for Article II, Section 1 purposes, regardless of the citizenship of their parents.”—September 6, 2012
http://judicial.clerk.leon.fl.us/image_orders.asp?caseid=77182640&jiscaseid=&defseq=&chargeseq=&dktid=57485906&dktsource=CRTV
That's simply not true. Both Minor and Wong Kim Ark separated natural-born citizens from "citizen of the United States at birth." They both said the 14th amendment does not define natural-born citizenship.
That's incorrect. See "7 FAM 1131.6-1 Status Generally" and "7 FAM 1131.7 Citizenship Retention Requirements" in the Foreign Affairs manual of the U.S. Department of State.
I agree that there are only two classes of citizens: born and naturalized. There are, however, multiple paths to each class, most with separate and distinct requirements.
I continue to say don’t look any gift horse in the mouth, perhaps it would be intelligent to modify that exclusion to something like American residency all of one’s adult life, you’re probably excluding some very competent and qualified patriotic people from being president while at the same time creating a distraction in the case of the current Resident, who is so clearly incompetent wherever it turns out he was born. I know from my own experience that being born in one country, moving to another at any early age, is almost identical in cultural experience to being native born. Yet people make such a big to-do about it when they find out, “oh you weren’t born here (wrinkle of the nose, etc)” like it matters at all. The nativist sentiment is very much at odds with the true meaning of exceptionalism and almost in a self-evident way, one would think.
There are more cases that uphold the natural born citizen requirement as distinct form citizen by birth than what you have cited. The history of the natural born citizen requirement is longer and more acute than your cited cases.
Natural Born Citizen is not equal to Citizen by Birth,
Natural Born Citizen is a subset categorization to Citizen by Birth. It is more restricted as intended by John Jay in his letter to General George Washingon.
Citizen by Birth is a superset and encompasses more citizens that those that are natural born or second generation.