To clarify: the right is the curls you create with heat, the left is after you carefully brush them out a bit so they appear more natural. So it's a before (well, mid way) and after, left to right. Most people prefer the natural looking styling.
I saw this a while ago on reddit, and the explanation in the comments was something about brushing the curls out for a more "natural" look, with the one on the right being worse for not doing it.