A screening test is, by definition, a test that is done to screen people who are at risk for developing a disease but have no symptoms of it. The goal of screening is to save lives by finding the disease early, before people know that they have it. The Pap test, for example, is a screening test used to identify women who have cells on their cervix that indicate they may be at risk of developing cervical cancer. Similarly, clinical breast exams and mammograms are done routinely on women who have no signs or symptoms of breast cancer to screen for the disease. The clinical breast exam may find a lump that a woman didn't know was present. The mammogram can detect microcalcifications, tiny deposits of calcium in the breast that may be indicators of breast cancer, or a tumor that cannot be felt through a clinical breast exam.
A diagnostic test is, by definition, a test done to help make a diagnosis once signs or symptoms of a problem have appeared, such as a lump, pain, thickening, nipple discharge, or a change in breast size or shape. A diagnostic mammogram uses the same mammography machine, but because the test is being used to detect a possible problem it usually takes longer than a screening mammogram as more X-rays need to be taken.