Did you find that "Gun" entry yet?
That's probably over your head, so I'll explain it to you in child terms.
Certain aspects of constitutional law are implicit and axiomatic. The reference to the word "Arms" in the constitution implicitly means all normal forms of weapons then in existence at that time. It doesn't have to SPECIFY each and every sort of Weapon meant to be covered.
In the same manner, usage of the term "Natural Born Citizen" is not intended to be specific regarding the means used to determine this status, so long as they are demonstrably accurate. The only requirement is to be provably accurate.
The Normal method for doing this in 1787 would be reference to Baptism records and perhaps the testimony of relatives.
Given that there has been some evolution since then, Certified Original Birth Certificates have become the Normal Way of demonstrating that someone was indeed born in the United States to American Parents, and is therefore regarded as sufficient proof that someone is a "natural born citizen" under even the most stringent criteria.
So to simplify the concept for your kindergarten level mind, "Arms" are to "Guns" what "Natural Born Citizen" is to "Verifiable Original Birth Certificate proof."
Got it?
More like you will need to have this explained to you more times than I care to do so.
I'm well familiar how "it is axiomatic" in DiogenesLamp-speak means "I'm making this up with nothing to support it other than my say-so."
When you come to terms with how "natural born" modifies "subject" in the analogous sense that "natural born" modifies "citizen," and that is why most all prominent legal commentators applied (and still apply) the birth-rule in the same way from one to another -- then you can perhaps start to claim credibility in comparing guns with birth certificates.
You're not out of the kindergarten level as to why "natural born" means the same thing consistently in English usage.
Certified Original Birth Certificates have become the Normal Way of demonstrating that someone was indeed born in the United States
No, the certified short form is what is normally used for DMV, passport, marriage licenses, etc. Copies of original (long forms) certificates are not the norm, due in part to medical information that is sometimes contained therein. That's why it was a big deal for Hawaii to let that out. It's not often done.
And neither form (long or short) purports to state the citizenship of the parents. You're again just making this up.