A brief story used in an essay to illustrate a point. example- "I remember there came into our neighborhood one of this class who was in search of a school to teach, and the question arose while he was there as to the shape of the earth and how he would teach the children concerning the subject. He explained his position in the matter by saying that he was prepared to teach that the earth was either flat or round, according to the preference of a majority of his patrons." Booker T. Washington Up From Slavery
A short story about an incident or situation that shows rather than tells. It may be as simple as an explanation or example or as involved as the retelling of an incident complete with a sense of plot and dialogue.
An anecdote is a short tale narrating an interesting or amusing biographical incident. It may be as brief as the setting and provocation of a bon mot. An anecdote is always based on real life, an incident involving actual persons, whether famous or not, in real places.