I think you mean “Nobel Prize” don’t you?

Prize and award are not really synonyms in many cases. Prizes are things you win in contests (like the winning Lotto number) and awards are just things bestowed on you for some achievement, not necessarily things you win in a contest randomly . There are exceptions. Like, you could be awarded money in a contest.  The phrase Nobel Prize is misleading in that it`s just a term of art. The Nobel Prize is an earned distinction, not something won by random chance. So, it just stands out as more of an exception than anything else. 

Adding to the other responses here: A prize is typically used to describe something won by chance.  If you got a toy at the bottom of a cereal box, you would call it a prize in English.  If you won the lottery they would call it your cash prize, or grand prize. An award is typically given to you based on your merit, or what you have earned.  Put another way, you enter a contest to win a prize. You are nominated to win awards.

Your example of the Nobel Prize is an exception to this and the use of the word "prize" is outdated.  Decades ago, it was common to win "first prize" or "the blue ribbon prize" - this was also the time that the Nobel Prize (proper noun) was named. There are other famous awards (notice this usage) in America/Europe that use the word prize as well (Booker Prize, Pulitzer Prize, etc). These would be referred to as awards. A completely appropriate sentence could read:  John was given the most famous award in the world, the Nobel prize.

Hope this helps!

Maybe a prize has some monetary connection, whereas an award does not?!

Nobel Prize has a $$ amount attached, Tony Award is a statue.