noun, plural her·e·sies.
- opinion or doctrine at variance with the orthodox or accepted doctrine, especially of a church or religious system.
- the maintaining of such an opinion or doctrine. Roman Catholic Church.
- the willful and persistent rejection of any article of faith by a baptized member of the church.
- any belief or theory that is strongly at variance with established beliefs, customs, etc.
“doctrine or opinion at variance with established standards” (or, as Johnson defines it, “an opinion of private men different from that of the catholick and orthodox church”), c. 1200, from Old French heresie, eresie “heresy,” and by extension “sodomy, immorality” (12c.), from Latin hæresis, “school of thought, philosophical sect.” The Latin word is from Greek hairesis “a taking or choosing for oneself, a choice, a means of taking; a deliberate plan, purpose; philosophical sect, school,” from haireisthai “take, seize,” middle voice of hairein “to choose,” a word of unknown origin, perhaps cognate with Hittite šaru “booty,” Welsh herw “booty;” but Beekes offers “no etymology.”
The Greek word was used by Church writers in reference to various sects, schools, etc. in the New Testament: the Sadducees, the Pharisees, and even the Christians, as sects of Judaism. Hence the meaning “unorthodox religious sect or doctrine” in the Latin word as used by Christian writers in Late Latin. But in English bibles it usually is translated sect. Transferred (non-religious) use in English is from late 14c.
This term’s use can often get foggy when speaking historically and is often confused with or treated equivalent to apostasy. Whether used to mean “sect” or simply any who are at odds with the official doctrine, the fact remains the same that those considered in heresy are outside the accepted doctrine.
Many Protestants would consider Roman Catholics as heretical though the same could just as easily be said in reverse. There are significant differences between the two despite their similarities such that you cannot truly consider them the same faith without ignoring significant differences.
Various other heresies would include (but not limited to): Deism, Docetism, the various Gnostic heresies, Arianism, prosperity gospel, LDS church (Mormon), and many more. Many of these and more would also be described as apostate at the same time.
See the apostasy link above for further discussion, compare/contrast, and other articles on this topic.