discreet means “not drawing unnecessary attention”: I trust you to be discreet about the unicorns in the back yard.
discrete means “separate”: The information was transmitted in discrete packets.

There’s a simple test for this pair. “Indiscreet” is the opposite of “discreet”, and will be in your spellcheck dictionary, but there’s no such word as “indiscrete”. Put an “in” on the front, and if spellcheck queries it, you have the one that means “separate”.