How do you figure a group of persons for whom you can't say to whom they were born is a class of persons??? This makes no sense. The two classes Waite was referring to was 1) Constitutional natural born citizens and 2) "citizens" as recognized by "some authorities" with no regard to the citizenship of the parents. There is doubt about the second class of citizens, but not the first.
Good. Now take the last step: "with no regard to the citizenship of the parents" is inclusive of those born of citizen parents. Thus, the "second class" is an expansion of (or, as Waite says, "going further" than) the first, not distinct and separate from it.