What is the difference between malnourishment and being underweight?

Malnutrition is the lack of proper nutrition; inadequate or unbalanced nutrition. Undernutrition is a nutritional deficiency resulting from lack of food or from the inability of the body to convert or absorb it.

For instance the substance called intrinsic factor is required for the absorption of the B-12 vitamin and this substance is produced in the stomach. After some surgeries like gastric bypass, the ability for the food to interact with the acid in the stomach is reduced and the absorption of B-12 is inhibited to the point where the body has a deficiency. This would be undernutrition. Not eating enough foods, or taking enough supplements to provide enough B-12 that would otherwise be absorbed would be malnutrition.