A censor hides information. A censure is harsh criticism. They're both judgments and they both stink.

Foul language, nudity, and revolutionary ideas are often censored, or hidden, by some gang who's in charge, such as a government, the FCC, or your parents when they kick you out of the room for the best part of the movie. Censor2020欧洲杯时间 can act as a verb or a noun:

But Iran routinely censors the Internet using sophisticated filtering technology. (Wall Street Journal)

The catalog reproduces a news photograph of "beach censors" arresting women in such offending garb. (New York Times)

Censure is a strong dislike. When you strongly disapprove of something, usually in an official capacity, you are censuring that something, like when the student council censures your idea to have a pool party in December. Here are more examples:

"They're tired of being censured or criticized," Dr. McKenna said. (Time)

While Maud, still smarting inwardly from her father's recent sharp censure, had not dared to brave Mr. Warren's certain anger by doing so. (Laura Dent Crane)

They sound alike but not the same: censor sounds like senser and censure sounds like senshure. Remember: to be censored is to be stopped from saying something; to be censured is to be reprimanded after you've said it.