An application shell is the enclosing page of a client side application. It stays open for the duration of the whole session. Such an enclosing page typically contains a header area, some kind of menu and a main area where the currently active component is embedded.
The purpose of the task concept is to realize the workflow of a given business process at one place instead of scattering the flow decisions and page sequences across all involved components. This makes reuse of components in different business processes easier, because the components need no knowlege about potential successors in the different workflows.