The Venus case did not involve natural born citizens - all three men involved were naturalized citizens - and therefore what constituted natural-born citizenship was not a matter before the court. Chief Justice Chase's comments were made in dicta and are not binding.
Of the three cases mentioned, only the Ark case actually touched on the question of natural-born citizenship. The argument was that he wasn't a citizen at all since he was Chinese and his parents could never be citizens under the laws in place at the time. The court found that under the 14th Amendment he was indeed a citizen by birth and the nationality of his parents was irrelevant to that. Since only two forms of citizenship are identified by the Constitution, and since he certainly wasn't naturalized, then obviously citizen by birth and natural-born citizen mean the same thing.
What did the Court in the Venus case understand the words “natural born citizen” to mean???? It is right there in the decision.