The most obvious difference between real essays and the things one has to write in school is that real essays are not exclusively about English literature. Certainly schools should teach students how to write. But due to a series of historical accidents the teaching of writing has gotten mixed together with the study of literature. And so all over the country students are writing not about how a baseball team with a small budget might compete with the Yankees, or the role of color in fashion, or what constitutes a good dessert, but about symbolism in Dickens.
That's no longer true at the university level. In fact, writing has been systematically dissociated from literary studies for a host of reasons, some political, some practical, as composition has established itself as a separate discipline. Only a minority of schools still link the two. (This isn't to say that writing courses aren't still grouped under the auspices of the English Department, only that literature, if it appears at all in a writing classroom, is used for reasons other than its literariness -- i.e. to introduce social issues, etc.)