Attention span seems to be more to do with how long we can focus on a particular task, video, game etc.
Patience seems to be connected to how long something takes before we perhaps intervene, so when working with children you need to give them time to complete a task, or if carrying out or learning something new you need to be patient so you can give your self time to really learn that and grasp that concept.
Be patient, and something will happen, useful for science experiments that may take a long time to complete for example.