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.

[0] https://www.law.cornell.edu/uscode/text/8/1101#a_21

[1] I think they can be.

[2] I'm very uncertain.

[3] <https://uscode.house.gov/view.xhtml?req=granuleid:USC-prelim...>

[4] <https://uscode.house.gov/browse/prelim@title8/chapter12/subc...>

    > Foreign national: A person without U.S. citizenship or nationality (may include a stateless person). This term is synonymous with “alien”