Students enrolled in online courses tend to be less successful as measured by the rate of A's, B's, and C's than students enrolled in face-to-face courses. Yet little work has been done addressing whether these gaps vary depending on students' broader relationship with the university, including whether they are degree-seeking students and whether they take any face-to-face courses. We use institutional data on Economics enrollments between 2012 and 2018 at a mid-sized land-grant university to deconstruct online/face-to-face success gaps into a student's term modality (or modalities) and institutional affiliation components. We identify these components by using a fixed effects regression methodology and comparing outcomes across four student groups: affiliated students who are enrolled in exclusively online courses, exclusively face-to-face courses, or in a mix of courses each term, as well as unaffiliated (external) students exclusively taking online courses. Although students in online courses are less successful on average, part of this gap is explained by the student's institutional affiliation and whether they exclusively take online courses. External students are the least successful in online courses while students who are affiliated with the institution fare much better. We examine potential reasons for these patterns using survey data from several online courses. These findings suggest that institutions should take steps to ensure that institutional support services and activities exist and extend to students in online courses.