Smampboy does raise a good caveat that athletic and need-based scholarships can have severe limitations. It does vary according to school and circumstance. Stanford says that the NCAA limits(at least in their situation) all need-based financial aid. However, the NCAA in its NCAA Guide for the Student-bound athlete states:
"The total amount of financial aid a student-athlete
can receive and the total amount of athletics aid a team can award may be limited. These limits can affect whether a student-athlete may accept additional financial aid from other sources. Ask financial aid officials at the college or university
about other financial aid you may be eligible to receive and about the impact of that aid on athletics aid limits."
The issue is more complicated than it appears and as the NCAA says check with the FA office at each school you are looking at. It appears that the spirit of the law is at limiting money coming in from third-parties or backdoors that don't count against the athletic department's scholarships while benefitting the student-athlete in a way that a non-athlete could not benefit.