This is another pair of homophones (words that sound alike but are different in meaning, spelling, or both) that can be very confusing. Discreet means that someone is showing respect and being reserved in their 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 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 show the differences between these two words:
“When Netflix hiked its price by a few bucks a month and tried to separate DVD rentals and online streaming into two discrete services, everyone was pretty annoyed.”
“Texting is more discreet than talking because what you text can’t be overheard by others, it’s private.”