What genre is a parable?

Answer 1

Well, I can tell you that a sub genre of a parable is the "exemplum" which is a story used to illustrate a point. Collections of exempla (exemplums is also acceptable) helped medieval preachers to enhance their sermons, to emphasize moral conclusions or illustrate a point of doctrine. The subject matter could be taken from fables, folktales, legends, or real history. Some places have listed Tolstoy's "The Death of Ivan Ilych" as an exemplum.

They can be called instructive traditional stories. They can be in prose or verse. They are a form of analogy.