Answer
See the detailed answer below.
Work Step by Step
The quantum number $ s $ refers to the intrinsic spin quantum number of an electron. Spin is a fundamental property of particles, much like charge or mass, and it describes the internal angular momentum of a particle. For electrons, $ s $ is always equal to $ \frac{1}{2} $.
This value is fixed and is not dependent on the state or configuration of the electron within the atom.
On the other hand, the value $ S $ is the actual vector magnitude of the angular momentum due to spin, which has units of J.s.
This value is given by using the quantum number $ s $
$$
S = \sqrt{s(s+1)}\hbar
$$
where $ \hbar $ (h-bar) is the reduced Planck constant.
