There were three categories for Greek plays: tragedy, comedy, and satyr plays. There was no 'drama' category.
In his Poetics, Aristotle defined tragedy as "an imitation of an action that is serious, complete, and of a certain magnitude; in language embellished with each kind of artistic ornament, the several kinds being found in separate parts of the play; in the form of action, not of narrative; through pity and fear effecting the proper purgation of these emotions."
As this note from email points out, Aristotle's definition may not make a lot of sense, so perhaps his example will help.
I read your by the book explanation of the difference about tragedy and drama, but I think that perhaps you could answer that youngster who asked what the difference is, with an example like: tragedy is what's happening in Iraq after the American invasion and drama is the story of the terrorist attack in Spain.
George Anastasoulis [April 6, 2004]
The train bombing in Spain was a despicable act and caused the loss of many lives, but it wasn't the act of people who were trying to do something helpful. The bombers can not be tragic heroes, so the event is not a "tragedy" in the ancient Greek sense of the word.