Yes, folks, it’s another descent into #HomophoneHell this time. By request, even–you can thank my pal Deborah Bancroft over at Dispatches from Wordnerdia.
First, let me assure you that at this point in time, there’s no danger of these words becoming hopelessly confused to the point of losing one to the other. Not yet, anyway. Garner’s Modern American Usage categorizes the confusion of “discrete” for “discreet” as Stage 1 (just about everyone can recognize it’s an error), and the reverse as Stage 2 (becoming more common, but still not accepted in standard usage; while it might appear as a variant in a dictionary listing, that hardly condones the usage.) I’ll suggest that people are generally more familiar with “discreet,” and so tend to use that one instead of “discrete” more often than they do the opposite. (The majority of my personal experience with “discrete” occurred in high-school geometry class.)
Let me remind you at this juncture that a dictionary (any dictionary) provides a snapshot of usage at a specific moment in time (the copyright year). Just because something appears in a dictionary does not mean that thing is correct, necessarily; it means that thing is common enough to merit an entry. Depending on the dictionary, there could be a usage note attached to such an entry indicating that it’s nonstandard (or a variant or what have you). If you want to be sure of having information about proper usage, you need a usage manual. All right. Onward.
“Discrete” means “separate.” “Discreet” means “cautious, circumspect.” Indeed, they come from the same Latin word: discretus. If you’re having several separate affairs, I suggest you be very cautious about discussing them with people lest they become intermingled (and thus neither discrete nor discreet).
As for a helpful mnemonic: The Es in “discrete” are separated by a T. Discrete = separate
(image thanks to Morguefile.com)