Reduction (gain of electrons) at the cathode, positively charged in a battery providing energy, negatively charged at an electrolyzing surface (e.g., something being plated with metal) consuming energy. Oxidation (loss of electrons) at the anode, negatively charged in a battery, positively charged at an electrolyzing surface (e.g., the metal source electrode for the thing being plated). REDCAT and LEO to remember it.
An electrochemical cell has separated internal reactive electrodes bathed in electrolyte that through chemical reaction create the electric potential across their external poles. The "charges" are extra electrons or holes in the band structure of the conductors. There is a lot of slosh in a conduction band compared to a discrete atom ionizing. There is little charge flow to equilibrium voltage. Connect the poles and current flows, limited by external and internal resistance, bracketed by reaction kinetics at the electrodes.
IMPORTANT! Current flow is opposite to electron flow (the negative sign in their charge).
An electron is a stable elementary particle that has measurable properties - mass, charge, a half unit of quantum angular momentum ("spin"); other observables derived therefrom. What an electron is, structurally, is undetermined as it appears to be a zero-dimensional point. Ask your instructor if an electron neutrino is an electron without its charge.