I have found a recent article which I found both short and very good. It covers .NET Standard, .NET Core and .NET Framework and their relationship. I highly recommend it. Unfortunately, I have no time to adapt and put it here.
Original answer content below:
So, based on the latest official entry on the subject, here are some key points as I see them:
.NET Core is essentially a fork of the .NET Framework whose
implementation is also optimized around factoring concerns.
We think of .NET Core as not being specific to either .NET Native nor
ASP.NET 5 – the BCL and the runtimes are general purpose and designed
to be modular. As such, it forms the foundation for all future .NET
verticals.
So .NET Native and ASP.NET 5 are just a test "subjects" for new framework configuration, partially this maybe because they are quite different:
See, they even need separate low-level, but a major part of BCL is still common:
We think of .NET Core as not being specific to either .NET Native nor
ASP.NET 5 – the BCL and the runtimes are general purpose and designed
to be modular. As such, it forms the foundation for all future .NET
verticals.
I.e., magenta rectangles on top will be added massively with new App Models, but the base will remain common.
NuGet deployment:
In contrast to the .NET Framework, the .NET Core platform will be
delivered as a set of NuGet packages. We’ve settled on NuGet because
that’s where the majority of the library ecosystem already is.
Relationship with current frameworks:
For Visual Studio 2015 our goal is to make sure that .NET Core is a
pure subset of the .NET Framework. In other words, there wouldn’t be
any feature gaps. After Visual Studio 2015 is released our expectation
is that .NET Core will version faster than the .NET Framework. This
means that there will be points in time where a feature will only be
available on the .NET Core based platforms.
Summary:
The .NET Core platform is a new .NET stack that is optimized for open
source development and agile delivery on NuGet. We’re working with the
Mono community to make it great on Windows, Linux and Mac, and
Microsoft will support it on all three platforms.
We’re retaining the values that the .NET Framework brings to
enterprise class development. We’ll offer .NET Core distributions that
represent a set of NuGet packages that we tested and support together.
Visual Studio remains your one- stop-shop for development. Consuming
NuGet packages that are part of a distribution doesn’t require an
Internet connection.
Basically this can be thought as a .NET 4.6 with a changed distribution model, which, simultaneously, is being in a process of becoming open source.