In trying to write such a short essay comparing and contrasting realism and naturalism in drama, you probably want to examine a limited number of salient points of difference. One way to make the topic manageable is to think of how naturalism functions as a narrow and extreme version of realism. In a sense, just as realism reacts against the "well-made play" of Scribe and Sardou, naturalism reacts against the conventions of realism.
Although both realism and naturalism portray "ordinary" people, the former emphasizes the middle classes and the latter the lower classes. Where the former is interested in the everyday, the latter is obsessed with minutiae. In staging, where realism moved costume and other sorts of staging to approximate everyday life, the minute particularity and scientific abstraction of naturalism can be seen as leading towards expressionism.