The ash is hard. The smell is acrid or harsh. Nylon is a polyamide made from petroleum. Nylon melts and then burns rapidly if the flame remains on the melted fiber. If you can keep the flame on the melting nylon, it smells like burning plastic.
Polyester is a polymer produced from coal, air, water, and petroleum products.
Polyester melts and burns at the same time, the melting, burning ash can bond quickly to any surface it drips on including skin. The smoke from polyester is black with a sweetish smell. The extinguished ash is hard. Rayon is a regenerated cellulose fiber which is almost pure cellulose. Rayon burns rapidly and leaves only a slight ash.