electromagnetism - Are the electrons spin and his magnetic dipole moment unambiguously connected?

Is the angle between the spin orientation and the magnetic dipole orientation for all electrons and under all circumstances the same?

Answer

The angle is the same as long as you consider a free electron. Then they are parallel:

$\vec{\mu}_\mathrm{elec}=-g_\mathrm{elec}\mu_\mathrm{Bohr}\frac{\vec{S}}{\hbar}$

with $g_\mathrm{elec}\approx 2$ (neclecting effects from quantum electro dynamics).

But when dealing with bound electrons (e.g. in an atom), where the electron also has some orbital angular momentum $\vec{l}$ things get more complicated and you have to consider the different contributions (weighting with g-factor) of the different angular momenta (including the spin).