AFAIK, major summer REUs are specifically designed for R1 research universities to host promising students NOT from their university, especially LACs but also “less research intensive” universities. They specifically cannot come from their own university nor from another R1.
Then, there are year-long research experiences (NSF or not) for students at the specific university (often Honors students or top students who stood out in specific courses or expressed an interest to the professor.) Undergraduates may not receive any stipend from their host institution by the way.
4 Likes