They could be interchangeable in some contexts but I would use them differently in other contexts. An inadequacy is any condition that is inadequate, insufficient, or not enough for a given situation. There might be inadequate food, shelter, confidence, support. These could be called inadequacies. A shortcoming is used more to describe some personal characteristic or some machine design flaw (or disadvantage). A person's shortcoming might be a character flaw (stingy, mean, selfish). An invention's shortcoming might be that it does functions A, B, and C, but it doesn't do function D. A shortcoming is more of a deficiency than an inadequacy. An inadequacy might be fixed by providing more resources, whereas a shortcoming is not so easily fixed. It would require a machine redesign (expensive) or a person to change their nature or character (not likely)