Module Zero Overall
ASP.NET Boilerplate framework is designed to be independent of any database schema and to be as generic as possible. Therefore, It leaves some concepts abstract and optional (like audit logging, session management and authorization) which requires some data store.
Module Zero implements all fundamental concepts of ASP.NET Boilerplate framework such as tenant management (multi-tenancy), role management, user management, session, authorization (permission management), setting management, language management, audit logging and so on.
Module-Zero defines entities and implements domain logic (domain layer). It leaves application and presentation layers to the application. You can use the startup template to create your application based on module zero.
Microsoft ASP.NET Identity Framework
Module Zero is based on Microsoft's ASP.NET Identity Framework. It extends user and role managers and implements user and role stores using generic repositories. It supports any ORM that can be used with ASP.NET Boilerplate (like Entity Framework and NHibernate). While module zero extends Identity Framework, it has many unique features.