Exemplify, illustrate are comparable when they mean to use in speaking or writing concrete instances or cases to make clear something which is difficult, abstract, general, or remote from experience or to serve as an instance, case, or demonstration of a point or matter under examination.
Exemplify implies the use of examples for clarification of a general or abstract statement or as aid in revealing the truth of a proposition or assertion.
Illustrate implies the use not only of concrete examples but also sometimes of pictures or sketches and the intent not only to clarify but to make vivid or real what is being explained or to drive home most effectively a point that is being made.