Can someone explain to me the difference between these two wiring configurations?
Looks to me like they are just saying, if you so choose, you may supply power to the two transducers from separate (isolated) power supplies. I'm guessing that would be a favorable approach if you wanted to ensure that the noise in the measurement from the transducers was independent and not coupled through the power source. But then, of course, you need two independent power sources to make that happen, which is not so difficult if we're talking about battery subsystems. Somewhat trickier if we're talking about AC/DC converters. 

You would need to experiment to determine your sensitivity in both measurements was "good enough" using a single power source.