Visual Studio 2017 References vs Dependencies
It's based on the project file type. The older Full Framework project file gives you the References area, whereas the newer project files give you the Dependencies area. In other words, as long as it's a .NET Framework 4.7 project, there's nothing you can do about it.
That said, you can simply make it a .NET Standard 2.0 project, which does benefit from the new-style project file. Really, all your class libraries should be targeting .NET Standard, anyways, for greater interoperability.
No you can't get the same treatment. It's because of the project type. Different types of projects have different tooling and features.
In the old days before Asp.Net Core, projects generally just had the References area, and you could have references to other Visual Studio Projects or to Dlls (your own or System Dlls).
But Asp.Net Core provides a different interface for this sort of thing and provides better tooling support for NuGet for example. For Asp.Net Core projects all this is organized below the Dependencies area.
But if you right click on Dependencies and select "Add Reference..." in your Asp.Net Core project, or if you right click on References and select "Add Reference..." in your .Net 4.7 Framework library you will see that in both cases you are presented with the same dialog. So there is still some commonality in the UI ultimately used to add a reference.