Check some of Newt Gingrich's writings, or those of other conservative writers, if you do not understand this point.
It is an EXTREMELY Liberal position to claim that only the Courts can make these determinations.
Next, in the case I spoke of, Madison clearly states that the CONGRESS has the power to determine who qualifies as a Citizen at Birth.
There are two types of Citizenship: Natural Born, or Naturalized. There are no other forms.
“It is an established maxim that birth is a criterion of allegiance. Birth however derives its force sometimes from place and sometimes from parentage, but in general place is the most certain criterion; it is what applies in the United States; it will therefore be unnecessary to investigate any other.”
James Madison, The Founders’ Constitution Volume 2, Article 1, Section 2, Clause 2, Document 6 (1789)
Madison is dead. He is sorely missed. But no matter, only the Constitution states what powers CONGRESS has.
As to you other red herring, it doesn't matter how many forms of citizenship there are. As a qualification for president, only "natural-born" citizens are eligible to hold this office. One must also be 35 years of age.
A [valid] birth certificate will establish one's eligibility for this office.