I hear people very often talk about “The Node Editor”. They often mention it in passing, while discussing other things. For newcomers like me, consistent terminology makes things that much easier to grasp. So I just wanted to check whether this Node Editor exist and if it’s something I’ve missed, apart from Shader Editor.
Almost always when people say ‘node editor’ they mean what is now called the ‘shader editor.’
The compositor does use nodes, but usually people refer to it as ‘The compositor’
Yes compositing nodes. Texture nodes. they are all using the nodal system. And also animation nodes. 
Why do your nodes look so weird? GPU driver issues?
Yes, i am only using my MacBook for test/examples, not on my PC right now,
And very soon there will be geometry nodes. But I agree with @digitvisions mostly it’s used for shading today.
In the Old Days it was The Node Editor and had Material, Texture and Composite window modes. That is legacy terminology, while those just recently entering the blenderverse most likely mean the Shader Editor.