Managed packages are typically used by salesforce.com partners to distribute and sell applications to customers. These packages must be created from a Developer Edition organization. Using the AppExchange and the License Management Application (LMA), developers can sell and manage user-based licenses to the app.
App: An app is a group of tabs that work as a unit to provide application functionality.
Package: A package is a bundle/Collection/container for a list of components or a related applications.