ASP.NET Core is a cross-platform, high-performance, open-source framework for building modern, cloud-based, Internet-connected applications.
ASP.Net applications developed on windows platform
whereas ASP.Net Core applications can be developed and run across different platforms like Windows, macOS, or Linux.
ASP.NET 4 applications can be hosted only on IIS, where as ASP.NET Core applications can be hosted on IIS, Apache, Docker etc
ASP.NET Core is fully open source and is being actively developed by the .NET team in collaboration with a vast community of open source developers. So, ASP.NET core is continually evolving as the vast community behind it is suggesting ways to improve it and help fix bugs and problems. This means we have a more secure and better quality software.