There is no difference really.
An exploded archive is a tree of folder and files that respects a given structure which your application server can exploit to deploy the application.
For a web application for instance, you create a war directory structure. The application server expects a WEB-INF directory containing the web.xml files which acts a a deployment descriptor.
A packaged archive is a zip file containing the above mentioned structure. The extension of a packaged archive can vary (war, jar, car, ear) but they are all zip files that contains a given structure.