The application of doping in semiconductors plays a major role in the high performances achieved to date in inorganic devices. In contrast, doping has yet to make such an impact in organic electronics. One organic device that does make extensive use of doping is the light-emitting electrochemical cell (LEC), where the presence of mobile ions enables dynamic doping, which enhances carrier injection and facilitates relatively large current densities. The mechanism and effects of doping in LECs are, however, still far from being fully understood, as evidenced by the existence of two competing models that seem physically distinct: the electrochemical doping model and the electrodynamic model. Both models are supported by experimental data and numerical modeling. Here, we show that these models are essentially limits of one master model, separated by different rates of carrier injection. For ohmic nonlimited injection, a dynamic p-n junction is formed, which is absent in injection-limited devices. This unification is demonstrated by both numerical calculations and measured surface potentials as well as light emission and doping profiles in operational devices. An analytical analysis yields an upper limit for the ratio of drift and diffusion currents, having major consequences on the maximum current density through this type of device.