Claudius is a Danish nobleman and the father of Laertes and Ophelia. He is a less major character in the play, but his murder by Hamlet in Act III helps to push the play much further along.       

Polonius is depicted as extremely distrustful, even of his own family, and always looking for a way to get ahead. He is so distrustful of them, in fact, that he even sends a spy after his own son, who is off to college in France! He frequently spies on Hamlet, which ultimately and indirectly leads to his untimely demise through Hamlet's sword.   

Polonius in the 1996 film. As a nobleman, he is well-dressed, but not as well as Claudius or Hamlet