Of course it means two classes of children. One class is "all children born in a country of parents who were its citizens." The second is "children born within the jurisdiction without reference to the citizenship of their parents." It doesn't take a law degree, just the ability to read plain English, to figure that one out.
The court isn't distinguishing between two kinds of citizens here. It did that in the previous paragraph:
the Constitution itself...provides that "no person except a natural-born citizen, or a citizen of the United States at the time of the adoption of the Constitution, shall be eligible to the office of President," and that Congress shall have power "to establish a uniform rule of naturalization." Thus new citizens may be born or they may be created by naturalization.So they just got finished saying that there are only two classes of citizens: born citizens and naturalized citizens. The next paragraph isn't further subdividing "born citizens," it's just noting that "born in the country of citizen parents" definitely means "born citizen," while "born within the jurisdiction without reference to the citizenship of their parents" might or might not mean "born citizen." But there's still only one kind of "born citizen," and it means the same as "native" or "natural born."
It's a meaningless distinction to say that it distinguishes between two classes of children but not two classes of citizen. The Constitution itself distinguishes between two classes of citizen. One, NBC, is a requirement for presidential office. The other, citizen of the United States (and a lesser class), is a requirement for Congress. That the court recognizes TWO ways citizens can be created, doesn't mean there is only one class of citizenship per way. One can be a citizen at birth via the naturalization statute, such as in the naturalization act of 1790.
So they just got finished saying that there are only two classes of citizens: born citizens and naturalized citizens.
It doesn't say "class" in this section, while it does talk about "class" in reference to NBC and those citizens recognized by "some authorities" who were born in the country without regard to their parents. The latter class of citizenship (of which there is doubt) lumps together both children born of citizens, and those NOT born of citizens. IOW, it's not two separate classes of children, but TWO separate classes of citizen: One is NBC and the other are born citizens whose citizenship would be in doubt.