USC - Anyone who applies by December 1st is considered for their scholarships including Trustees (which you interview to try to get after being notified you are a finalist). Notification is end of January, with interviews over the next several weeks. Getting a scholarship does not obligate you to commit in any way. USC does not have ED.
BU - I know nothing about BU but after a little web surfing, you apply by December 1st for scholarship consideration, completing an essay just for the Trustee Scholarship. Notification appears to be in March. ED application dates are Nov 1 and Jan 3 (for ED1 and ED2) so the scholarship essay has it’s own submission date.
A binding decision to attend only comes into play if you applied ED and are accepted, it is not tied to getting a scholarship. Separate processes.
Does this make sense?