I) The main point is that when we apply Noether's theorem for a field theory, the
total angular momentum Noether current
$$J^{\mu,\nu\lambda}~=~L^{\mu,\nu\lambda}+S^{\mu,\nu\lambda}$$
splits in an orbital angular momentum current $$L^{\mu,\nu\lambda}=x^{\nu}T^{\mu,\lambda}-(\nu\leftrightarrow \lambda)$$
and an internal spin angular momentum Noether current $$S^{\mu,\nu\lambda}~=~\frac{\partial {\cal L}}{\partial \Phi_{,\mu}} \Sigma^{\nu\lambda}\Phi,$$
where $\Sigma^{\nu\lambda}$ furnishes a Lorentz representation of the field $\Phi$ in the field target space. For further details, see e.g. Ref. 1.
II) In particular for a scalar field theory, there is no spin, $\Sigma^{\nu\lambda}=0$ is generators for the trivial representation, and the angular momentum is generated purely from infinitesimal variations in spacetime, cf. e.g. this Phys.SE post.
References:
- A. Bandyopadhyay, Improvement of the Stress-Energy Tensor using Spacetime symmetries, PhD thesis (2001); Chapter 2.