My understanding of magnetic fields was that the strength of the field was "path dependent". I.E. the $\mathbf{B}$ field decreased more when it went through materials with relative permeability close to 1 as compared to ferrous materials with much higher relative permeability. (I.E. magnet -> wood -> some point in space would have a lower B field than magnet -> iron -> some point in space). I guess I got this idea because outside of electromagnetism permeability means "the state or quality of a material or membrane that causes it to allow liquids or gases to pass through it." So I assumed it was the way the magnetic field passed through a material, and how the magnetic field turned out on the other side of that material.
But then I started reading https://www.maxwells-equations.com, and now my whole world is turned upside down. Specifically because of this line: "In Equation 1, permeability is the permeability of the medium (material) where we are measuring the fields." (emphasis added). So it doesn't matter what is between the magnet and the point? It only depends on the distance and the material itself?
This Question and answer seem to indicate the magnetic field is indeed "path dependent". But I'm not sure if they're talking about the H field or the B field. In other words, are the "insulators" mentioned in the question messing with the H field, and then to get the B field you must multiply by mu of the last material, or are they "insulating" by reducing the B field (in which case, are the B and H fields really distinct, or just a mathematical construct?).
