I am having a hard time understanding what happens at equilibrium in an electrochemical cell (a full cell with two electrodes). At equilibrium, according to Nernst equation, the cell potential is $E_{cell}=E^0_{cell}-\frac{RT}{zF}lnQ_r$. Is this cell potential equal to the voltage of the cell ? At equilibrium, the voltage is zero, so does it mean that $E_{cell}=0$ and that both half cells have the same potential ? I am confused about this, as I also understood that $E_{cell}$ at equilibrium is the electromotive force of the cell, which means that it isn't zero.
Thank you for your help !