The award is always associated with something good. Award is used as both noun and verb
As a noun – Award is a prize for recognition of an achievement
As a verb – Award is giving something for recognition of that achievement

The reward does not necessarily have to be a physical entity. It can be monetary, word of praise, love etc. A reward is also used as both Noun and Verb.
As a noun – it is a contingent benefit for an action.
As a verb – it is something that is given to someone for doing an action.