You need to ask the financial aid officers at the schools. It can vary widely. The way I have most seen it done is that financial aid does cover off campus living either in one schedule or having a separate schedule for such cases. Greek housing is considered off campus housing. But that is not always the case
However, there are often separate rules for where a student can live under certain circumstances. Schools that need to fill housing may require students to live on campus. They may also require them to take a meal plan, sometimes there is no choice as to which meal plan. Yes, there can be different rules for athletes, financial aid, scholarship students.
If you are in a tight budget, it is important that you know these policies. At some schools, the financial aid schedules are a one size fits all, and that can be a problem when upperclassmen housing is more expensive than freshman housing, yet the aid is given on averages. Also, if you are required to live on campus, it can be more expensive for you than living off campus in certain areas. These things all can make a difference to the bottom line.