Distributed use case 

This one is mainly used with core infrastructure services or the like, where an instance of the application can run on the public cloud and another instance of the same application can be in-house/private cloud. 

As an example, take the case of Active Directory. We could have the secondary AD on the public cloud, which will start serving the applications in the public cloud, however they remain in-sync and the public cloud is treated as another site in the Active Directory Sites and Services.