Greek theater was the origin of theater. In fact, the origin was speculated upon by those to whom we now attribute the origin of theater such as Aristotle. Greek theater developed both comedy and tragedy, with a preference for tragedy, the guidelines for which were famously defined by Aristotle. Roman theater was an imitation of Greek theater, but there were some cultural differences. Romans preferred comedies to tragedies. Women were allowed onstage but only in mimes, or plays or sections of plays with no dialogue. One thing Greek and Roman theater shared in common was the wearing of masks. Firstly, they allowed a limited number of actors to play multiple roles that were differentiated by a change in mask. Secondly, masks symbolized types of characters thus could represent young, old, happy, sad, etc.
You can google examples of amphitheatres to see something of what #2 is talking about. There is a fine example still standing in Epidavros which I had the good fortune to go and visit. You will also want to focus on the role of the Chorus in your response to the question. What is interesting about Greek plays such as Oedipus Rex is the way that the Chorus acts like another character that is involved in the action but also separate from it and free to comment upon it. This is an interesting dimension that is largely absent from Roman drama.