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The iPhone app only shows the items which are already overdue (current date/time is past the due date/time), whereas the desktop app also shows items which will be due in the future, with the precise behavior depending on your view bar/perspective settings.

There's a feature in the works that will allow you to see your actions in their context from the Overdue list, etc. It got pulled from 1.6 at the last minute, but hopefully it will be back soon! You can see it in the new Perspectives feature where it didn't get removed.