For U. S. tax filing purposes the following are consider U. S. persons
A citizen of the U.S., including someone born in the U.S. but living in another country, who has not renounced or otherwise relinquished their U. S. citizenship.
A lawful resident of the U.S., including a U.S. green card holder
A person residing in the U. S.
Someone spending a specified amount of time in the U.S., potentially including “snowbirds” who spend winters in the Florida or other warm climes.
A green card holder who never formally handed in their green card upon leaving the U.S. (even though the green card in no longer valid for U. S. immigration purposes).
The child of a U. S. citizen provided a parent lived in the U. S. period for a specified time period (with some exceptions, see T Dott comment)
All of the above would be affected by FATCA. Financial Institutions will also look for indicia including:
A U. S. place of birth
A current U.S. residence or mailing address ( including a U.S. PO Box)
A current U.S. telephone number
Standing instructions to pay amounts from a foreign (meaning non U.S.) account to an account maintained in the United States
A current power of attorney or signatory authority granted to a person with a U.S. address
A U.S. “in-care-of” or “hold mail” address that is the sole address with respect to the account holder
Others affected by FATCA include any non U.S. person who shares a joint account with a U.S. person or otherwise allows a U.S. person to have signatory authority on the account.
Any business or not for profit organization that allows a U.S. person to have signatory authority on a financial account.