Runtimes -> This runs the IL code, includes Mono, CLR, and CoreCLR. Mono was written by Miguel Icaza to support cross platform mobile development. CoreCLR is a new version of the CLR that supports .NET core code.
Libaries/Frameworks -> .NET core, .NET framework. Two different versions of the libraries, .NET Core is newer and cross platform but older technologies such as webforms can't run on it, .NET framework supports older technologies but isn't cross platform. Plenty of libraries are usable inside either framework.
Ahead of Time Compilation Technologies -> .Net Native, CoreRT, AOT
Most new devs don't have to know any of this to be productive. Just pick .NET core unless you need to use .NET Framework for backwards compatibility reasons.
Libaries/Frameworks -> .NET core, .NET framework. Two different versions of the libraries, .NET Core is newer and cross platform but older technologies such as webforms can't run on it, .NET framework supports older technologies but isn't cross platform. Plenty of libraries are usable inside either framework.
Ahead of Time Compilation Technologies -> .Net Native, CoreRT, AOT
Most new devs don't have to know any of this to be productive. Just pick .NET core unless you need to use .NET Framework for backwards compatibility reasons.