Would someone please explain the difference between the two and why to use one over the other??
Pastillige is a lot stronger, and is used more for construction, or anywhere where the pieces need to be extra strong, like for a standing plaque or standing picture frame or something like that. If you were building a gumpaste house to put on top of a cake, for example, you would probably get on better if you used pastillage for the wall panels and roof, as it's stronger than regular gumpaste. (Having said that I don't use pastillage myself for construction - I make mexican paste and mix that with a little bit of fondant and that works perfectly for me)