It’s both. The electron $g$-factor within an atom contains a term proportional to the electron spin, and also a term proportional to the electron’s orbital angular momentum quantum number. In an atom with an unpaired $s$-wave electron, there isn’t any orbital angular momentum, so only the spin contributes. But if a valence electron has nonzero $L$, the orbital state contributes to the atom’s magnetic dipole moment as well.
For example, in iron, there are two unpaired d-shell electrons which contribute to ferromagnetism. However, beware that chemists label the relevant states $d_{z^2}$, which has $m=0$, and $d_{x^2-y^2}$, which is a superposition of $m=\pm2$. The orbital magnetic moment is proportional to $m$, and vanishes if you use the non-complex wavefunctions in which projections like $m=+2$ are unavailable.