Q. What are the functional differences between Windows 2012 Storage Server and the Windows Server 2012 Standard and Datacenter editions' functionality?
A: There are no functional differences. In the past, the Storage Server SKU of Windows Server had additional features such as iSCSI target and single-instance capabilities. However, in Windows Server 2012 there are no feature differences. Windows Storage Server 2012 exists as an OEM-only solution that's used on storage appliances. But it has no functional advanctages over the standard Windows Server 2012 SKUs.
The goal of Storage Server is to enable OEM partners to provide Windows-based storage appliances with all the capabilities of Windows Server 2012, such as Storage Spaces, data deduplication, SMB3, iSCSI, ReFS, and more, in an easy-to-deploy-and-maintain appliance form factor. If you're building your own server, then there's no benefit to using Storage Server (nor can it be licensed separately) and you should use Windows Server 2012 Standard or Datacenter.