Censor is someone who examines things for non-conformity or possible evil. It also means to examine and to subject a book, writer, etc. for suppression or prevention from becoming known, when it is regarded as objectionable for any reason: “The censor board banned the film as it contained objectionable content.”
Censure, on the other hand, is an act of condemnation or to make a formal, often public statement of disapproval of somebody or something: “To censure someone publicly is a big risk, it can cause a lot of trouble for both the parties.”