The following are the two types of assemblies:
Private Assembly - Refers to the assembly that is used by a single application. Private assemblies are kept in a local folder in which the client application has been installed.
Public or Shared Assembly - Refers to the assembly that is allowed to be shared by multiple applications. A shared assembly must reside in Global Assembly Cache (GAC) with a strong name assigned to it.
For example, imagine that you have created a DLL containing information about your business logic. This DLL can be used by your client application. In order to run the client application, the DLL must be included in the same folder in which the client application has been installed. This makes the assembly private to your application. Now suppose that the DLL needs to be reused in different applications. Therefore, instead of copying the DLL in every client application folder, it can be placed in the global assembly cache using the GAC tool. These assemblies are called shared assemblies.