Discrete and Discreet

This is one of those word mix-ups that you can have a lot of fun with, because the examples can be very funny.

Discrete means separate, either in separate parts or separate from external influence. 

Discreet means keeping your mouth shut about something.

I took a class in high school called discrete math. Discrete math deals in "countable sets," like how many apples are in a bag.* It's the opposite of continuous math (like calculus) which can handle concepts like imaginary numbers or infinity. "Infinity apples" is not a countable set; you can't count infinity apples.

That's not infinity; that's, like... twenty.

My discrete math teacher (meaning the math was discrete, not the teacher... that's a horrifying thought) thought it was terribly funny when people wrote "discreet math." "Shh! We're doing math! Tell nobody!"

Or, if you prefer a non-math example:

The baker cut the cake into twelve discrete slices discreetly, telling nobody about it.

*Discrete math does a lot more than this, but for my purposes, this is a sufficient explanation. Also, I took the class a decade ago; I don't remember it all.