The difference is in the material in the bead. Steel wire is usually used on the cheaper tires and it is not good to kink that. The ones that come in the boxes folded are made of kevlar fiber instead, which won't take a kink or set. Nonetheless I still like to unroll them and let them relax out for a while before installing. I would not however put a wire bead tire into the same package size.
You can however put a Wire bead tire into a circular fold by twisting it over itself. This is how other wire things such as band saw blades are shipped in smaller packages. It is not as small as the kevlar tire package, but it won't harm it either.