Azure Stack essentially is Microsoft’s better bridge to using its cloud services, both the platform-as-a-service (PaaS) and infrastructure-as-a-service (IaaS) kinds. It uses the same code as Azure.
Scripting tools for management, such as PowerShell and command-line interfaces, will work across Microsoft’s Azure cloud computing services as well as local datacenter implementations of Azure Stack. This allows a company to build a private cloud, and then easily migrate parts to a public cloud, allowing you to have a true hybrid cloud platform. Microsoft is the only company to have both a private and public cloud option.
