The stage server and main production site are completely independent environments and have different databases. All the account_ids, user_ids, application_ids, application tokens, etc. are different between stage and production environments. Each environment has its own set of endpoints as well.
After you test your application on stage, you will need to create the application on production and use the production application ID and secret to connect to the production environment.
Please note that the stage server does not process move "real" money and, for example, allows the use of "fake" credit card numbers for testing.