cotton also burns with only a little smoke if any and the ash - if any - is very soft and powdery. The ash, if no fire is seen with cotton, cools down quickly.
polyesters and nylons burn with black smoke - they also leave a hard "crispy" ash. Sometimes it "drips" while burning. The residue also stays hot longer than cotton residue. One can still get burned with this residue, even if the fire is out.