What is the difference between wood pulp-based materials and rigid materials?

Maybe it’s the way the question was asked, but these two aren’t mutually exclusive.

Wood pulp-based materials are any composite using wood fiber. Fiberboard, cementitious fiberboard, OSB, plywood… There are materials people still call fiberglass when the fiber is actually wood fiber.

Rigid can be tough as it doesn’t have a universal definition. Some materials are rigid because they support their own weight while other definitions call materials rigid under certain loads or types of flexure.