Is the Self Consistent Field an actual field?
The notion of a self-consistent field comes from the orbital approximation - that a multi-electron wavefunction can be approximated as multiple one-electron wavefunctions.

At that point, the question remains - how does each of those electrons interact with the remaining $N-1$ electrons?

Well, there's an electric field from the electron density, right? Maybe you want to call this an electrostatic potential -- but Hartree considered it a spherically-symmetric electric field.

The problem, of course, is that since you don't know the final charge density, you have to make a guess and iterate until it's "self consistent."

Thus, SCF has been associated first with HF theory, and other related methods, including Kohn-Sham DFT.