[sten]

this should explain it:

native born == born within the US
natural born == a native born person born of two US parents

followed by:
“Every human being born within the jurisdiction of the United States of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen. (Cong. Globe, 39th, 1st Sess., 1291 (1866))”

note:
“of parents not owing allegiance to any foreign sovereignty”

[Ha Ha Thats Very Logical]

this should explain it:
native born == born within the US
natural born == a native born person born of two US parents

Not really. You cited a reference to "that provision in the constitution which requires that the president shall be a native-born citizen." But the Constitution says "natural born," not "native born." So how can your quote be right unless natural born and native born mean the same thing?