Content is managed then staged (rendered and packaged into zips) on AEM-AUTHOR and published (zips replicate to) to AEM-PUBLISH. Apps running on DEVICE can check for and pull app content updates (the packaged zips) from AEM-PUBLISH.
AEM Mobile Apps (using OnDemand Runtime)
Content is managed then uploaded from AEM-AUTHOR to AEM OnDemand hosted services. AEM-PUBLISH is not used (in a typical deployment) given AEM OnDemand is managing the published content. Apps running on DEVICE can check for and pull app content updates from OnDemand services.