Award refers to an official prize given to someone for something he has done. Reward refers to something given to someone because he has done something good or helpful.
award She has received an award as Teacher of the Month. Last year’s award was given to Dr. Smith. Stay at our award-winning hotel and enjoy your stay!
reward His mother has given him a reward for passing all the exams. Our school has a system of rewards to encourage hard work. A reward of $100,000 has been offered for giving the police information about the criminal.