Named after it's inventor, the Clerihew has given Edward Clerihew Bentley a small niche in the history of literature. Bentley, born in 1875, invented the Clerihew when still a teenager. As an adult he wrote detective stories and articles for The Daily Telegraph.
The Clerihew is 4 lines long, with aabb rhymes, and always about a person (or possibly an animal). The first line always ends with the name of the subject. There are no rules about metre. They should be fun.
An Epigram is a short, clever verse or saying - 2 or 4 lines. They can be funny, but don't have to be. Often they have a folky sort of wisdom