I've written[0] and spoken[1] a lot about .NET Core, so I understand that it can be confusing. The similar naming certainly doesn't help. To summarize (and oversimplify) there are three main varieties of .NET: .NET Core, .NET Framework and Xamarin.
The new open source and cross-platform one is .NET Core and it is currently suited to writing server-side web apps (e.g. ASP.NET Core) and command line applications. It is a reimplementation of .NET and more use cases are coming (UWP, CoreRT, native tool-chain etc.).
The Windows only one is .NET Framework and it is better for graphical desktop apps on Windows. WPF and Windows Forms are not open and are Windows only, so are not in .NET Core.
Finally, Xamarin is also open now and lets you build native mobile and desktop apps on Android, iOS and macOS. Full details of all these are on the official docs site[2] if you want to read more, or you could buy my book on ASP.NET Core 2 :).
[0]: https://unop.uk/book/
[1]: https://unop.uk/talks/
[2]: https://docs.microsoft.com/en-gb/dotnet/