"Significant" is hard to quantify. Obviously, Load Range D has more capacity than Load Range C. 'C' is basically a passenger car tire. 'D' is a light truck tire. I don't know of any way to compare performance, but the Load Range D tires will have stiffer sidewalls and ride harsher on pavement.
As for construction, you have to review each manufacturer's specs for the tires you are considering. In general, I would expect a Load Range D tire to have two more lies, but that's not always the case.