Location and visibility:
A private assembly is normally used by a single application, and is stored in the application's directory, or a subdirectory beneath. A shared assembly is normally stored in the global assembly cache, which is a repository of assemblies maintained by the .NET runtime. Shared assemblies are usually libraries of code which many applications will find useful, e.g. the .NET framework classes.
The runtime enforces versioning constraints only on shared assemblies, not on private assemblies.