How does the idea of magnetic fields arising from circulating currents relate to permanent magnets?

The same statement applies, but in the case of a permanent magnet, the currents are electrons circulating atoms in orbits such that there is a net magnetic moment for each atom (often iron), and many of the atoms are aligned with magnetic axes pointing in the same direction. Only a few elements (such as iron) and alloys (such as alumimum-nickel-cobalt) have this behavior.