There are two separate but related quantum numbers associated with intrinsic angular momentum ("spin"). The first one, ##s##, is associated with the
magnitude of a particle's spin: ##S = \sqrt{s(s+1)}\hbar## which for an electron equals ##\sqrt{\frac 1 2 \cdot \frac 3 2}\hbar = \frac {\sqrt 3} 2 \hbar \approx 9.14 \times 10^{-35}~\rm{kg \cdot m^2 / s}##. This is a fixed, unchangeable value which (like the mass) is the same for all particles of a given type, e.g. 1/2 for electrons.
The second one, ##m_s##, is associated with the
orientation (direction) of the spin, specifically with the component of the spin along any given direction, which we customarily call the "z-component" although it doesn't have to be actually along the z-direction: ##S_z = m_s \hbar##.
##m_s## can have one of the values ranging from ##-s## to ##+s## in integer intervals. For ##s=\frac 1 2## (e.g. for an electron) these values are ##m_s = - \frac 1 2## ("spin down") and ##m_s = + \frac 1 2## ("spin up"). For ##s = 1## they are ##m_s = -1, 0, +1##, for ##s=\frac 3 2## they are ##m_s = -\frac 3 2, -\frac 1 2, +\frac 1 2, +\frac 3 2##, and similarly for other values of ##s##.
For an electron, ##S_z = \pm \frac 1 2 \hbar \approx \pm
5.28 \times 10^{-35}~\rm{kg \cdot m^2 / s}##.
Note that the spins of the electrons in a chunk of metal contribute to the chunk's total macroscopic angular momentum, as shown in an experiment described in
chapter 37 of the Feynman Lectures on Physics, specifically, Fig. 37-3 and the preceding paragraph. This is known as the
Einstein-de Haas effect.