Difference between mean and expected value

#1
Could someone please explain as simply as possible the difference between mean and expected value?

Here is my problem: This is for my math stats class. I have read the textbook and done several of the problems in the probability distributions chapter. I understand how it works, basically (or at least, I know how to use it).

Where I'm stuck is that in the instructions for the project I have do, the instructor uses the term "mean" for a discrete probability distribution problem. (It is a comparison of the population and a sample we create on our own - at least I think that's what it is. All the possible outcomes vs. the outcomes I got.) Example: "Find the mean and standard deviation of this discrete random variable." Is it normal to just use the terms interchangeably?
 
#3
Okay, that helps a bit, thanks. I think I'm still doing something wrong but I can't figure it out with her using "mean" the whole time.