There are many more names for things in C# than what you really need to be aware of as a C# developer. Want to write C# that targets Linux? Download the .NET Core SDK. Simple as. Everything else: .NET Standard, .NET Framework, are just names used by the .NET contributors to keep things straight in their head, but you honestly rarely deal with that stuff if you’re starting fresh with .NET Core.
If you’re trying to write C# in emacs you’re doing it wrong. C# has probably the best tooling in the world if you embrace it.