Most wool coats are labeled dry clean only. Often the lining has padding to prevent stretching and these inner fabrics are not machine washable. If placed in water the material can dissolve or become misshapen. A wool coat is best cleaned by a dry-cleaning professional and not laundered on your own.
A waterproof jacket has a finish on the material to make it waterproof. When laundering this type of coat, it is best to use a delicate cycle and cold water with a gentle laundry detergent (specifically for delicate items.) Do not tumble dry these coats, air dry as the dryer can harm the waterproofing.