What is the difference in this specific breadboard wiring?
In the second arrangement, both legs of the LED are on the same horizontal row - In breadboards, each set of 5 holes on either side of the board is shorted together.

In other words, your LED's legs are shorted together, no current will flow through it.

See this image of how a breadboard's holes are typically connected internally:

 (source)

The red thin lines indicate internal connections between the respective holes. 

For a more detailed discussion on breadboards see this answer. 



Specific to the Fritzing software the images in the question seem to be made in: 

Note that as soon as any lead of a component is inserted into a hole in the on-screen breadboard, all the holes that are internally connected get a green indication - That shows that those holes are essentially electrically connected to the occupied hole.