Are Williams-Exeter students Williams students, or Oxford students, or both?
Both. They remain Williams students while in Oxford and the tutorial work they undertake in Oxford counts towards their degree requirements (and is calculated in their GPA) back at Williams. Nevertheless, they are formally Visiting Students at Oxford University, with an Oxford University ID (in lieu of a Williams ID), subject to many of the rules and regulations of Oxford University and enjoying most of the benefits of the University that are enjoyed by fully matriculated Oxford undergraduates.