Interaction between two resting charges (electrostatic case - in electrostatic field) is anyways electromagnetic (because we have only 4 fundamental interactions). Electromagnetic interaction means exchange of photons ("carriers" of Electromagnetic interaction).
How does this exchange happen? When and how these photons are created, moved and how they disappear? Say, in case of just two electrons (two elementary charges).
P.S. I am also puzzled that not moving charges in one referecne frame are moving in another reference frame, so same interaction can be viewed as "electrostatic" or electromagnetic depending on reference frame.
Besides I do not understand why we ever speak of electrostatics if even in electrostatic case essentially (deeply) real physical interaction is electromagnetic (electrodynamic, exchange of photons).
In case of macro-bodies (two big charged bodies) I don't know how we ever can speak of "electrostatic" fields because all elementary charges (electrons, ions, etc) forming those bodies are moving - and moving implies electromagnetic, not electrostatic.
P.S. This discussion adds to this topic.