The adjectives discreet and discrete can easily be confused in writing, for various reasons. First, when typing quickly, the second e may just slip in before the t. Because both words exist, this mistake will not be detected by the spell checker. However, in addition, the pronunciation of discreet and discrete is identical, see here and here, so many people may just be unaware of the very different meanings. The Oxford Learner’s Dictionary provides the following explanations:
discreet: careful in what you say or do, in order to keep something secret or to avoid causing embarrassment or difficulty for somebody
discrete: independent of other things of the same type
An example for the use of discreet is given by the sentence
“I discreetly glanced at my watch during the meeting”,
meaning that I looked at my watch in a way so as to hide my action from people around me. Similarly, you can be discreet about a love affair, or a bill.
On the other hand, the use of discrete can be illustrated by the sentence
“Cats and dogs are discrete species”.
In mathematics, discrete is the opposite of continuous. For example, the set of integer numbers is discrete (there are no numbers between 1 and 2), whereas the set of real numbers is continuous.