You are correct. The proceeds of student loans, being money that you are legally obligated to repay, are not income, and have no impact of your tax return. You can use the proceeds for anything. 

Scholarships, on the other hand, are income. If used to pay qualified post-secondary tuition and fees, books, and required materials, the income is tax-free. If used to pay for room and board, travel, recreation, and other expenses, the income becomes taxable.

For more information, please see IRS Pub. 970 Tax Benefits for Education.