Nick, it’s very simple. If we’re just talking about NEED-BASED aid (not merit), financial aid is awarded based on your ability to afford the cost of attendance (COA). COA includes tuition, room, board, mandatory fees, books/supplies, and personal expenses. For every college in the U.S., those are the components of COA. Need-based financial aid does not distinguish among these various components. They just determine – based on their own formula – what your family can afford to pay.
The second thing you need to understand is how universities bill you. You don’t get a bill for tuition and then a separate bill for room &board. You get one master bill from the college that will include tuition, room & board, and mandatory fees. The other components of the COA are paid by you on an as-needed basis (with your own money or with financial aid funds that are provided).
Merit is a different story. You can get a flat-rate merit award, such as, say, $25k. It doesn’t matter which components of COA it covers. It’s $25k toward your COA overall. Some colleges structure their merit as full tuition or half tuition or “full ride” (which can mean total COA or total of tuition, room, and board).