ASP.NET Core is a free and open-source web framework, and higher performance than ASP.NET,[3] developed by Microsoft and the community.It is a modular framework that runs on both the full .NET Framework, on Windows, and the cross-platform .NET Core. However the expected version ASP.NET Core 3 was announced to work only on .NET Core dropping support of .NET Framework
The next version of ASP.NET which is Open source and cross-platform framework. Core apps can run on both on .NET core as well as full .NET framework. Web apps, mobile apps and IoT apps can be created.