Question

How do representational, abstract, and nonrepresentational artworks differ?

Answer 1

Non-representational means it doesn't show a realistic image of what it is trying to portray - that can mean it is abstract or cubist or even impressionist. 
Representational means that an everyday person looking at the picture will say  it looks real.
Abstract, is the extreme, that nothing about the work has to represent anything - it can show just color, just a blob or just lines. you get the picture ;P lolNon-objective is representational and may show things which look real but distort real scenes or come out of imagination.