The terms are definitely interchanged often and there isn’t a huge difference. Cord is a more overarching term that can be applied to a variety of materials that come in long strands. They may or may not be twisted, braided, or woven. Rope falls under the category of cord and involves many fibers being twisted, braided, or woven together to create a workable cord. We use 3-ply twisted ropes for our 5mm and up, 2-ply twisted ropes for our thinner 3mm ropes, and our string is made of 1 strand of twisted fibers.
In our upcoming book, we differentiate ropes as being the material before it is cut, and cords as the material after it is cut, as in your «working cords» or «filler cords» for when you are making your project. Otherwise it is just up to you what you want to call it!