They are different tenses, but they are used in this case to mean the same thing. It is much more common to hear "What are you doing on Saturday?" even though they are speaking about the future. If they simply said, "What are you doing?" This can only refer to the present. If they simply said, "What will you be doing?" This can only refer to the future. However, because the word "Saturday" is used in the sentence, "What are you doing on Saturday?" the listener knows that the speaker is referring to a future point in time. That is why in this case they are able to use the present tense to discuss a point in the future. To correct the second part of the question: "Do* both of these* sentences* mean* the same thing*? Can I use either* one* of them? ..Please tell me the difference*. I usually hear people using the first one.* What about the second one?* Is it * advanced* English?"

Hi, I'd like to be language partners on italki. I'm Ron in New York, USA. I'm happy to help you improve your spoken English. If you need help, please add me to your Skype: ron.jenkins86 And if you want a new friend, lets be friends! :) Thanks and see you soon!

As Luke said, they mean the same thing using different tenses.... the important thing being that you put "on Saturday" on the first one to indicate you mean future time and not right at the moment. :)