What is the difference between the American Opportunity Credit and the Lifetime Learning Credit?

The American Opportunity Credit (AOC) gives up to $2,500 per student for the first four years of post-secondary education; 40% ($1,000) is refundable. The Lifetime Learning Credit gives up to $2,000 per tax return (not per student) and applies to any post-secondary courses, with no limit on the number of years — but it is nonrefundable. AOC phases out at higher income levels and cannot be used if the student has a drug conviction.