What does the m symbol for magnetic flux mean? Why is it needed when the phi symbol exists?
m is the mass of one ferromagnetic material which was equated from two possible masses m1,m2 into one.  The Magnetic potential,M has been defined by the energy per pole of magnetic flux per unit in the magnetic H field.  The flux phi can be derived as the mass drawn into that measured H field both controlled by the gap, r.
A relevant Wiki definition follows but is more relevant to Maxwell's equations than mass.
That is for static permanent magnets, similar to static charges in insulators=dielectrics which have an E field and forces inverse to radius r for parallel plates, cylindrical or flat.
E fields are for voltage/m and H fields are for currents/m.
The energy equivalence is 1/2 CV^2=1/2 LI^2, which in ideal LC components causes perpetual motion of charges at a resonant frequency. Yet ideal parts never exist due to a series R.
For electromagnets, coils, chokes and inductors
https://en.wikipedia.org/wiki/Magnetic_scalar_potential