Foreign national is anyone who doesn't have legally recognized citizenship of the USA. So citizens living abroad aren't barred, nor would dual citizens be.
> What is a “foreign national” is more what I’m wondering.
The following quoted text is from the Definitions section of 8 USC § 1101, which is reproduced at [0]. (Though, you will probably have to scroll up a bit to be able to read subsection (a)(21), which is the thing I'm linking to.)
(21) The term “national” means a person owing permanent allegiance to a state.
(22) The term “national of the United States” means (A) a citizen of the United States, or (B) a person who, though not a citizen of the United States, owes permanent allegiance to the United States.
(23) The term “naturalization” means the conferring of nationality of a state upon a person after birth, by any means whatsoever.
From this, it's fairly clear that a "foreign national" is someone owing permanent allegiance to a foreign (that is, non-US) state. What's not immediately clear to me is whether a US citizen can also be a "foreign national", [1] and how that would affect access to things from which foreign nationals are barred. [2]
EDIT: For a more official source of this information, you might be able to check out [3] and/or [4]. After examining and interacting with those pages, one might see why one might go to an unofficial source for casual inspection of this information.
A "foreign national" is any person who is not a US Citizen:
"The United States Department of State defines a “foreign national” as anyone who is not a “U.S. person.” A “U.S. person” is any one of the following: U.S. citizen; Lawful permanent resident (green card holder); and “Protected Person” i.e. political asylum holder." [0]
A foreign national is a person or organization who is not a citizen of the United States, and who is a citizen of a foreign country. The Immigration and Nationality Act (INA) uses the term "alien" to refer to a person who is not a United States citizen, and does not use the term "foreign national."[1]