As far as I understand, .Net Framework is the fully framework we know and love with all the Windows implementations and lots of code we don't normally use, like they explain in some videos an XML parser.
In .NET Core they removed all the unneeded implementations/dependecies and only left the basic ones. which also enables cross platform (not yet), so in the future one could think as the only framework : CORE Framework, and run on any device. Their february community standup give a lots of information and insight on their objectives and goals.
I see this as a transition, when some features are available only on the full Framework while in the futures one might expect to see all features available for .NET Core.
From a Microsoft perspective, if they want to release lets say Entity Framework for mobile (EF7 is aiming at that) they must get rid of all the windows implementations, on EF and it's dependencies (Framework). So they created a non-windows dependency on the framework, which also helps the multiple framework install and remove some problems with updating the framework by having them mostly isolated from the system, lying in the application. New problems will come like multiple copies of the same framework on one machine per application, that's why they are working on something called Smart Sharing.
This post may help you and give you some insight specially this part :
The structure of .NET Core is comprised of two major components which
add to and extend the capabilities of the .NET Framework as follows:
- Runtime:
Built on the same codebase as the .Net Framework CLR. Includes the
same GC and JIT (RyuJIT) Does not include features like Application
Domains or Code Access Security. The runtime is delivered on NuGet
(Microsoft.CoreCLR package)
- Base class libraries:
Are the same code as the .Net Framework class libraries but do not
contain dependencies so have a smaller footprint. Available on NuGet
(System.* package)
and I guess you already read Introducing .NET Core from Microsoft.
Regarding your concern about specifying a specific framework is because right now, not everything works on Core CLR so you must choose which one to use, or you can target both and use different implementations.
As of right now, CORE only runs on Windows; the mono framework doesn't have a SQLLite provider for entity framework but it does on Core, so you can use an InMemory or Azure EF provider for example, and choose depending on the enviroment your application is running.
As Scott Gu says on the community standup, they envision a future where there's no mono framework or full framework, there's just Core, but that will take time if it ever happens.