The precision has meaning. The 1790 act used the exact same wording - "natural born Citizen". Since the ONLY reason for "natural born" is for Presidential qualification the tie-in in inescapable. It was a direct tie to AIIS1.
I agree that the act did not by itself 'define' "natural born Citizen". But it indicated what was CONSIDERED the key criteria - jus sanguinis. I believe that the act was an attempt to somewhat override AII. It did this by ignoring or downplaying jus soli. Even the infamous SR 511 mis-states that this act 'defined' natural born Citizen.
The act was not repealed as much as replaced and simply omitted. I have never found a specific, verified reason for the omission in the 1975 act. One theory, and it is only a theory, is that the error of overriding AII via a law or act was not proper was recognized by Congress and thus this override was dropped.
But during the 5 years in was in effect it provided not just 'citizenship' to those born overseas to parents who where already citizens. It provided codified law to 'consider' those born only under the rule of jus sanguinis 'as' natural born Citizens. As pointed out the child would still need to live within US at some point to claim their citizenship. But if they did do that and then met the 'Citizenship' requirement the act gave them claim to the 'natural born' criteria and thus they could be President and CiC.
In summary, there is an ongoing argument - strongly argued today - that 'natural born Citizen' has never been formally defined. In the strictest sense that is true. But this act, that was even cited in SR 511 (though slightly incorrectly) provides insight that jus sanguinis WAS (and IS) part of the definition. But only part. But this part seemed to be considered dominiant of the two parts typically argued - jus soli and jus sanguinis. Blood is thicker than dirt to the Congress of 1790.
Of course it was.
From the text of the 1795 Naturalization Act:
"Section 4. And be it further enacted that the act entituled [sic] "An act to establish an uniform rule of naturalization," passed the twenty-sixth day of March one thousand seven hundred and ninety, be, and the same is hereby repealed."
While in the confines of one’s own thoughts shortcuts like “AIIS1” or “AII” make sense, what stops you except laziness to make the meanings clear and not abbreviations to those who do not occupy the same physical space between your own ears?
Talk about PRECISION!