Those who were naturalized, and those who are born here in the US. Thre rest is just junk.
You left out the category of those who are born in another country of American Parents, such as Aldo Mario Bellei of Rogers v Bellei. You also left out derived citizenship. Prior to the Cable act of 1922 and the Women's citizenship act of 1934, any woman married to an American male obtained derivative citizenship from her husband automatically.
Also, for most of our History the Children of naturalized citizens obtained derivative citizenship from their father.
You seem to be of the opinion that this is all simple and cut and dried, but if you research the issue you will discover this is not at all the case. In ex parte Reynolds the court concluded that the sole governing factor was the citizenship of the father. They specifically invoke the principle "Partus Sequitur Patrem". (The Father's country is the child's country.)
statutory exceptions which prove the rule.
McCain had to be suject to a statutory exception in order to fit into the citizenship rule.
as for deriving only from the father, in this day and age that is laughable as we do not even allow a widows only share of inheritance, we have widow’s or widower’s share for inheritance.
again there are only two types of citizen NOT three.
You are correct. Herbert Hoover’s foreign born mother as well as Woodrow Wilsons foreign born mother were made U.S. citizens by derivative marriage to their American born husbands. That made both Hoover and Wilson natural born citizens at their births with born sole allegiance to the United States.