ASP.NET is a part of Microsoft .It is a web development platform. ASP and ASP.NET are server side technologies .
ASP .NET Core is across platform,high performance,open source framework for building modern,cloud based internet connected application. you can use build web apps and services,IoT apps and mobile back ends ,use your favorite development tools on windows,macOS and Linux,Deploy to the cloud. IoT(Internet of Things) is the inter-networking of physical devices,vehicles,buildings and other items embedded with electronics,software,sensors network connectivity that enable these objects to collect and exchange data.
ASP.NET is an open-source server-side web application framework designed for web development to produce dynamic web pages. It was developed by Microsoft to allow programmers to build dynamic web sites, web applications and web services.
ASP.NET Core is a free and open-source web framework, and the next generation of ASP.NET, 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.
Open source cross platform development environment
Open source stable environment for web development
ASP.NET Core is a new open-source and cross-platform framework for building modern cloud based internet connected applications, such as web apps, IoT apps and mobile backends. ASP.NET Core apps can run on .NET Core or on the full .NET Framework.