The National Institute of Diabetes and Digestive and Kidney Diseases wrote in their Mar. 2006 publication "Lactose Intolerance":

“Lactose intolerance is the inability to digest significant amounts of lactose, the major sugar found in milk. Lactose intolerance is caused by a shortage of the enzyme lactase, which is produced by the cells that line the small intestine. Lactase breaks down milk sugar into two simpler forms of sugar called glucose and galactose, which are then absorbed into the bloodstream. Not all people deficient in lactase have the symptoms commonly associated with lactose intolerance, but those who do are said to have lactose intolerance.

People sometimes confuse lactose intolerance with cow’s milk intolerance because the symptoms are often the same. However, lactose intolerance and cow’s milk intolerance are not related. Being intolerant to cow’s milk is an allergic reaction triggered by the immune system. Lactose intolerance is a problem caused by the digestive system.”

Mar. 2006