Honours are distinctions normally conferred by a government or a head of state. Example: the U.S. Presidential Medal, a Knighthood of the British Empire. Awards are just prizes. The first prize in a primary school colouring competition is an award. An Oscar is an award. It is true that "honours" are often misused on a host of trivial prizes in trivial competitions.

An 'award' is something which is normally given to you by someone else (or by a group). A classic example is the acting profession, who are given awards such as the Oscars. It is not certain which actors will win awards. Even those who give the best performance of their lives may not receive an award. An 'honor' (or 'honour' in British English) tends to be more automatically given in recognition of doing something. So if a person does x, they will get honor y. I used the word 'tends' in the above paragraph, because the distinction between the two is often blurred. The British Queen gives our honours to people for things they have done. Perhaps winning in their sport, or acting, or helping the community, or for service to the British State...but it is never absolutely guaranteed who will get such an honour. Like many things with English, the context is key. I hope this helps a bit.