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Re:Announcing .NET Core 1.0 by chinhodado on Monday June 27, 2016 @12:11PM (#11987117)
The general idea of .NET as a platform is easy to understand. The naming of .NET Core, .NET Framework, ASP.NET, etc. and the difference between them is not.
Re:Announcing .NET Core 1.0 by oblio on Monday June 27, 2016 @12:25PM (#11987224)
.NET Framework = the whole shebang, the full runtime including Windows-only bits.

.NET Core = portable subset of .NET Framework. Therefore not entirely compatible with .NET Framework.

ASP.NET Core = portable rewrite of ASP.NET. AFAIK not fully compatible with previous versions.

Re:Announcing .NET Core 1.0 by cobalt on Monday June 27, 2016 @03:29PM (#11988785)
iirc asp.net core does not contain the web framework part, just the server stuff