Yes, changing the W has a similar effect as changing X, Y and/or Z in the Mapping Node.
You can think of a 3D Noise as a 4D Noise with constant W. Think of the function with 4 variables; when one of the variables is constant, then you have a function with 3 variables.
The W, X, Y and Z are just the names of the variables in that noise function.
As to your question above: you can achieve a similar effect with a 3D Noise Texture in various ways. I would probably do something based on this:

Is that what you meant?