This is another pair of homophones (words that sound alike but are different in meaning, spelling, or both) that can be very confusing. Discreet implies the showing of reserve and prudence in one’s behavior or speech. Discrete means something quite different: “distinct, separate, unrelated.”
Both words derive from the same Latin word discretus meaning “separated.” Until the 1700s, these words were each spelled many different ways including discrete, discreet, dyscrete, discreete, etc. Eventually discrete and discreet came to be differentiated in spelling as well as in meaning. Discreet has yielded the noun discretion, but discrete‘s noun form is discreteness. For most of English history, discreet was more frequently used, but today discrete is much more frequently used than discreet; it has seen a dramatic rise since the 1940s according to Google nGram.
Here are a few useful examples that exemplify their differences:
“They balked when the company hiked its price a few bucks a month, and they absolutely howled when Netflix tried to separate DVD rentals and online streaming into two discrete services.” –Matt Peckham, “Netflix Was Right, and We’re Being Fickle,” Time, October 25, 2011
“The beans, too, are not the usual congealing muddle, but discrete drops of heirloom yellow-eyes, scented with coriander.” –Ligaya Mishan, “Salsa, Flirting With Bok Choy,” New York Times, April 3, 2014
“Munro is a great writer; a wise writer; a free and brave, exacting, transformative, generous, and profoundly discreet writer.” –Gish Jen, “Alice Munro, Cinderella Story,” The Daily Beast, October 12, 2013
“It makes sense because texting is more discreet and can’t be overheard…” –Lily Hay Newman,” Crisis Hotlines Now Offer Texting With Counselors,” Slate, February 10, 2014