At least in respect to aeronautical engineering the difference is the same as the difference between potential and dynamic. Fatigue assessment, usually done in the development of a structure, is the potential for a component or structure to fail due to fatigue, whereas fatigue crack growth assessment is the discovery, maintenance and monitoring of a fatigue induced crack. The usual method of maintenance of fatigue cracks that are allowed is to stop drill them to relieve the stressor and then monitor for continued propagation...