Can you tell me the difference between a bone density test and a bone scan?

Yes. Bone density tests measure the amount of calcium in the bone to determine a person's risk for fractures. Bone scans use a radioactive tracer to identify areas of abnormally high cellular activity in the bone. Some conditions that may show up on a bone scan include recent fractures, infections of the bone, or some forms of cancer in the bone.
Density v Metabolism. In general, the bone density test is used to evaluate for possible osteoporosis, and response to osteoporosis therapy. The bone scan is used to evaluate bone metabolism, primarily to detect bony metastatic cancer and also to evaluate the cause of bone pain (cancer, stress fracture, muscle, etc).