Discreet is probably the more familiar word, and is usually used to refer to people, especially their speech, appearance, or behaviour. It means unobtrusive, circumspect and prudent, careful not to attract attention or cause embarrassment, able to keep a secret. Discretion is the noun form. You could think of the adjacent e’s in discreet discreetly sharing a secret: they couldn’t do this with a t in the way.
She promised to be discreet with any sensitive information.
As the meeting began, he yawned discreetly.
Discrete generally means separate, non-continuous, individually distinct; it also has technical usages relating to possible parts or values. Discreteness is the related noun. To remember this spelling, think of the t separating the e’s and keeping them distinct from one another.
A sentence is composed of discrete words.
We divided the work into discrete sections.