It is often mentioned that the density of angular momentum of an electromagnetic field is given (up to constants) by the expression (e.g. in the Wikipedia page): $$\mathbf M\equiv \mathbf r\times(\mathbf E\times\mathbf B).\tag A$$ We also know that there are two "types" of angular momentum that an EM field can carry: spin and orbital angular momentum. At least from a quantum mechanical perspective, these are quite different beasts: the spin being an intrinsically two-dimensional degree of freedom, while the orbital one being related to the spatial distribution of photons/light.
I wonder, from a classical perspective, does (A) account for both spin and orbital angular momenta? Is there any easy way to see this?