Do Claudius & Polonius have the same reasons for spying on Hamlet & Ophelia? How are their goals similar in Hamlet? How are they different?

In Shakespeare's Hamlet, Claudius and
Polonius, on the surface, have the same reasons for spying on Hamlet and Ophelia, but
only on the surface. 

Both Claudius and Polonius are trying
to figure out why Hamlet is "mad," or acting insanely.  Polonius believes that Hamlet's
behavior is due to his love for Ophelia being rejected by Ophelia (which he put her up
to in the first place).  He is trying to prove his theory to
Claudius.

Claudius wants to know if this is the reason for
Hamlet's insanity, too.  In this respect, Claudius and Polonius are similar.  But
Claudius has a further motive, as well.  He is trying to keep an eye on Hamlet and
figure out Hamlet's behavior, so he can judge whether or not he is in danger from
Hamlet. 

Claudius, of course, has recently kept Hamlet from
inheriting the thrown by marrying Gertrude, and has also "replaced" King Hamlet
as Hamlet's father, at least technically.  Neither of these make Hamlet happy.  Claudius
wants to know if Hamlet is so upset due to Ophelia's rejection, or due to the other
recent events.  Claudius is hoping that Ophelia's rejection is the cause of Hamlet's mad
behavior.  If that is the case, then Hamlet is no threat to
him. 

Of course, according to Hamlet himself, his behavior
is all an act, a smoke screen, if you will.  Hamlet says that he is only pretending to
be mad, in order to, we assume, keep Claudius busy worrying about his madness, rather
than about Hamlet's plans for revenge.  Hamlet's madness is a
diversion.