Exemplar, not Example

Sometimes it is difficult to tell, because those two have meanings which very much overlap. Both came from the same Latin root, from the verb meaning to take out, perhaps to exhibit as an example. Both can refer to a typical instance (Monet's Impression: Sunrise is an example of Impressionism), or a similar instance (US involvement in the Vietnam War may have provided an example for Bush's headlong charge into Iraq).
But exemplar can also refer to the archetype, the original model of something (the extended real plane is the exemplar, not just an example, of projective geometry), whereas example has no such meaning. That is the essential difference. The original model, versus just another model. So even though the adjective is exemplary, only example is used to refer to conduct worthy of imitation. It is as if the adjective referred to a Platonic ideal of conduct which cannot be reached, only approached, by imperfect concrete examples in the real world.