How does Yale define an International Student?

As @gibby pointed out, Harvard and Yale do not publish those statistics. My guess is, although it will vary by colleges, a US citizen who moved abroad after birth, a dual national born in the US but currently living abroad, and a dual national born and living abroad will often be lumped together as US citizen living abroad for classification purposes. Their chances for admission, again only my opinion, will be roughly the same as an applicant born and raised in the US. The odds for a “true” international applicant will certainly be less, if MIT’s acceptance rate for intl applicants vs. domestic applicants are any indication.
http://mitadmissions.org/apply/process/stats