.NET Core and Mono are two different implementations of .NET Standard.
It's a standard as described in the name.
The standard is either CLR (Common Language Runtime) or CLI (Common Language Infrastructure), I'm not entirely sure.
Edit As far as I can tell, yes, even Miguel de Icaza is consistently misusing these terms.
Edit 2 - Nope, I'm wrong!
https://docs.microsoft.com/en-us/dotnet/standard/net-standar...
(Yes, there are also ECMA standards for the CLR/CLI, C# language, and a somewhat small subset of the BCL [Base Class Library]. .NET Standard subsumes those underlying standards and then specs out a much larger set of the BCL and even some libraries that aren't strictly BCL but may as well have been in the way they've become standards such as ADO.NET.)