These words are pronounced the same, and they are both adjectives.
Discrete means separate, distinct, individual:
- The two companies have a partnership, but they are discrete entities.
- We offer three discrete service plans: internet only, internet + cell phone, and internet + cell phone + TV.
Discreet describes something that is modest and does not call attention to itself:
- The photographer at the funeral remained discreet and respectful.
- She discreetly adjusted her bra strap, which was falling down her shoulder.
When you describe a person as discreet, it means that person can handle sensitive topics with tact (good manners and professionalism).