It might be said that the main difference is that American Literature was discovering unique topics. It might be characterized by Puritan´s ideas and belief. There could be found some sermons and short stories. As regards, British literature, it might be said that it implied poetry and essays and later on the birth of the novel.
Lead to confusion or misunderstanding
it depends on what type of play it is but mostly the central idea will be around one or two main characters and the trials that they go through