Do Claudius and polonius have the same reason for spying on hamlet and Ophelia? How are their goals similar? How are the different?

Not at all. Polonius wants to find out what is best for his daughter and believes that Hamlet's madness is based on his rejected love for Ophelia. Claudius believes that Hamlet's madness may be an act and that he may know that Claudius killed Hamlet Sr. and that Hamlet could want to murder Claudius.