Smoking can affect the leg arteries in different ways. The arteries supply less blood to the muscles, leading to pain while walking. The commonest smoking-related disease of the legs is called Buergers disease, and this is probably the diagnosis that your doctors have made. Another possible disease is Atherosclerosis, which has many causes, and is worsened by smoking. Both these conditions affect the arterial supply to the legs. In occasional patients amputation of the legs is needed, therefore smoking must be stopped. The diseases thus are smoking-related, although the cause is not really a deposit of nicotine.
Smoking causes hundreds of diseases in the body. The diseases of the legs are some of the lesser problems. Anybody can get the diseases, but there is no way to tell which smoker will get which illness. Smoking-related illnesses come from the hydrocarbons in the smoke, and from the nicotine.