Our rights and the rights of others is often the topics of discussion. Whether we are speaking about how other people have violated our rights or that certain rights should be given more protection.
Here, A and B are persons and X is a situation.
Example: B borrowed $100 from A. So A has a claim right against B that B returned $100 to A.
Example: If A the right (against the Japanese Government) to stay in Japan, then this is a privilege. It means that the Japanese Government has no claim-right against A that he leaves the country. Or in other words, A has no duty to the Japanese Government that he leaves Japan.
Example: The librarian has the power over a student with regard to the use of the library. Normally a student has the right to use the library. But if a student is noisy then the libarian has the power to take away that right and stop the student from using the library.
Example: Diplomats are supposed to have diplomatic immunity. If they have committed a crime in their host country, they are immune against arrests and legal prosecution. In other words, the police would have no power over them. (They can still be expelled though.).
For more information of types of rights check out these sites.