Heresies are beliefs that do not agree with the official beliefs of a particular religion; heresy is the maintaining of such contrary beliefs.
Heresy can be used figuratively: To disagree with the school committee's decisions is considered pure heresy by the faculty. This noun is from Middle English heresie, from Old French, from Late Latin haeresis "school of thought, sect," from Greek, "action of taking, choice," from hairein "to take, choose." A person who believes or speaks heresies is a heretic.