An award is a special prize such as the Oscar. It is usually connected to a contest or social event. A reward can be anything you get for making an effort, or as an incentive, say like cash back in credit cards, or miles, even a small cookie for "being good."
An award is an honor (such as a medal or trophy) that is conferred for merit, usually after a decision made by a committee of judges
A reward is something (usually money) given in return for a person's service, merit, hardship, etc.