The skin worm (Gyrodactylus) gives birth to living young and therefore is capable of fast reproduction.  This results in skin irritation and the thickening of the skin and your fish produce a slimy mucous layer over their skin
The gill worm (Dactylogyrus) is a parasite that lays eggs.  It causes damage and irritation to the gills with your fish gills thickening and them losing their function.  Infested fish often rub their gills on plants and stones.