The first is .NET Core which is a smaller subset of the .NET framework. .NET Core was largely for web apps and web workers, but it was announced yesterday that soon .NET Core will support desktop applications as well. Not all assemblies are available in Core, but it has a smaller package size and will run on any platform.
.NET Framework is the one people usually refer to when they say ".NET", which is the full-featured framework that is used to build VB.NET and C# applications.
A great read about the difference in use for server applications (which is where the real details lie) can be found here.