In The Tempest, what are the differences between Prospero's and Shakespeare's plays?
I have had to edit your question because you asked two questions. Please remember that you are not allowed to ask multiple questions.
If I understand your question correctly, you want me to comment on the relationship between Prospero and Shakespeare and the fact that in this play we have several plays-within-a-play. This of course is not something that is restricted to this play alone. In Hamlet plays-within-a-play are a central part of the plot, as "The Mousetrap" is intended to provide proof of the guilt of Claudius. Certainly what it does seem to do is present Prospero as the director of the action on the island.
Much has been written of how Prospero represents power in the play. He is on the stage longer than any other character and he is shown to control the fate of all characters on the island. Nothing happens without him willing it or being aware of it, and a central issue to consider is if he uses his powers with wisdom or in a selfish fashion. Plays have varied in their depiction of Prospero as a magnanimous ruler or a sadistic oppressive coloniser, and clearly there is evidence for both of these options. However, the masques that are featured as part of the action in this play rather seem to strengthen the sense of power that Prospero holds. There seem to be many comparisons that we can make between Prospero and Shakespeare: both direct the action and are in control of their characters, having their destiny in their hands; both use a variety of different forms of "magic" in their dramas and both participate in their own dramas (let us remember that Shakespeare himself acted).