An “award” is a prize that you receive for having done something noteworthy. It is always associated with something positive; you have done something which people approve of. It is a sign of appreciation. You could be awarded a medal, a prize, or a certificate by an organisation for an outstanding achievement. When judges bestow an award on you, they are honouring you.
*The only award that Neelam ever won was the Pulitzer Prize.
A “reward”, on the other hand, is usually associated with something valuable — money, for instance. You may get a reward for finding and returning someone’s dog/cat. The police may offer a reward for information about an escaped convict. It is seen as something that you get as just compensation for the good that you have done or the hard work that you have put in. For example, if you have worked really hard to write a novel, and later you receive an award for it, you may feel that it is a recompense for all the work you put in, that it is a reward for your effort. While the word “award” is associated with only positive things, “reward”, on the other hand, can be associated with both good and bad. One can be rewarded for the evil one does as well.