Form 8863 is used to calculate education credits. It is used for both the American Opportunity Tax Credit and the Lifetime Learning Credit. The Lifetime Learning Credit offers 20% credit for the first $10,000 of qualifying education expenses.
Regarding Form 8917 for the Tuition and Fees Deduction, this is calculated "above-the-line," which reduces income. The adjusted income is eventually taxed. In contrast, the credit is subtracted directly from taxes owed.
For more details, see:
Lowdown about education credits
