Not according to Donofrio.
Naturalized - born on foreign soil and took on American citizenship.
Native Born - born on American soil of one or two non-citizens. My son is native born as my husband is Canadian and I am American. Our son was born on American soil.
Natural born - Born on American soil of two American citizens. Either the parents are both born on American soil, or the parents can be naturalized, but the child must be born after the parents take on citizenship.
Curious, you have any good sources about “native born” citizenship? Its not a got-you question, I honestly want to learn more.
In an early draft of the constitution Hamilton wrote “No person shall be eligible to the office of President of the United States unless he be now a Citizen of one of the States, or hereafter be born a Citizen of the United States.” This is the earliest draft of the natural born requirement for presidency, and I believe its consistent with my interpretation.