What are .NET Core & ASP.NET Core?
They are fully open-source frameworks under the .NET Foundation; commonly used with C#, VB.NET and F# languages which are all also open source and designed on GitHub.
They run on the open-source “Common Language Runtime” which has the aim:
The goal of the CLR is to make programming easy - from the Book of the Runtime
.NET Core and ASP.NET Core were born in the open-sourcing of .NET and the reimagining of ASP.NET; which also took them from Windows only to cross-platform; additionally supporting macOS and flavors of Linux, BSD and adding ARM to the supported chipsets.
The .NET Community has embraced the open-sourcing of .NET; and its progress has never been so vibrant. A .NET renaissance has begun!
Source: https://www.ageofascent.com