The courts have interpreted the terms “natural born citizen” and “Citizen of the United States At Birth” to be synonymous over the last 117 years. No court and no action of Congress has ever stated anything different. If a person qualifies as a 14th Amendment Citizen of the United States At Birth under the current law of the land (8 USC 1401) then they are also an Article II, Section 1, Clause 5 natural born citizen as well.
For example: Tisdale v. Obama, U.S. 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, U.S. District Court of the Eastern District of Virginia, January 23, 2012.
and: Allen v Obama, Arizona Superior Court Judge Richard E. Gordon: “Arizona courts are bound by United States Supreme Court precedent in construing the United States Constitution, and this precedent fully supports that President Obama is a natural born citizen under the Constitution and thus qualified to hold the office of President. Contrary to Plaintiff’s assertion, Minor v. Happersett, 88 U.S. 162 (1874), does not hold otherwise.”—Pima County Superior Court, Tuscon, Arizona, March 7, 2012
or: Taitz v. Obama (Quo Warranto) “This is one of several such suits filed by Ms. Taitz in her quixotic attempt to prove that President Obama is not a natural born citizen, as is required by the Constitution. This Court is not willing to go tilting at windmills with her.”— Chief U.S. District Court Judge Royce C. Lamberth, U.S. District Court for the District of Columbia, April 14, 2010