This type of assembly is used by a single application. It is stored in the application's directory or the applications sub-directory. There is no version constraint in a private assembly.  

Shared Assembly or Public Assembly

 A shared assembly has version constraint. It is stored in the Global Assembly Cache (GAC). GAC is a repository of shared assemblies maintained by the .NET runtime. It is located at C:\Windows\Assembly OR C:\Winnt\Assembly. The shared assemblies may be used by many applications. To make an assembly a shared assembly, it has to be strongly named. In order to share an assembly with many applications, it must have a strong name. 

Differences between Private and Shared Assembly

• Private assembly can be used by only one application.
• Shared assembly can be used by multiple applications
• Private assembly will be stored in the specific application's directory or sub-directory.
• Shared assembly is stored in GAC (Global Assembly Cache).
• There is no other name for private assembly.
• Shared assembly is also termed as shared assembly
• Strong name is not required for private assembly.
• Strong name has to be created for shared assembly.
• Private assembly doesn't have any version constraint.
• Shared assembly should strictly enforce version constraint.