These words are sometimes confused because the expression a cult often sounds like the word occult.
Cult most commonly means a religious sect organized around a strong leader and requiring beliefs or commitments not typical of other related groups. It can also refer to a following of a particular religious figure or icon within an organized religion or a fanatical following of a particular entertainer, athlete, film, television show, or historical figure.
Cult is normally a noun, though it can be used as an adjective meaning "having a cult following" as in ia cult film.
Occult literally means "hidden" and generally refers to the pursuit of some kind of magic or secret supernatural knowledge or power. It is most often used as an adjective but is sometimes used as a noun.
The verb to occult means "to hide from view," and is used most commonly in scientific or specialized fields such as astronomy, navigation, or optics.