Confusion between positive and negative terminals of a battery

Outside a battery, current flows from its positive terminal to its negative terminal. Inside the battery, to stop charge building up, the current must flow the rest of the way round, from the negative terminal to the positive terminal. This flow is driven by the chemical reactions in the battery.

In an electrolysis cell the current flows through the cell from the positive terminal to the negative terminal. The same applies for any other component which does not generate its own emf.

Current always enters a device though the anode, and leaves though the cathode, so it flows through the device from anode to cathode. That means that for a normal device the anode is positive, but for a battery the cathode is the positive terminal.

The anode is defined as where oxidation happens, the cathode is where reduction happens. The mneumonic is Cations are reduced at the cathode and anions are oxidised at the anode.

When oxidation happens electrons are produced(on the products side of the reaction) thus these electrons come out of the anode and flow towards the cathode. Electrons are repulsed out of the anode and flow towards the cathode, the electric field/current is of course in the opposite direction. During electrolysis the negative terminal of the voltage source is connected to the cathode where reduction will happen with the incoming electrons, and the positive terminal of the voltage source is connected to the anode where oxidation will happen. Electrolysis is like a battery charging as the reactions are reversed from the discharging galvanic cell, during discharge the anode produces electrons and is the "negative" terminal. During charging you connect the negative to the negative and the positive to the positive, technically the anode becomes the cathode and the cathode becomes the anode because the reactions are now reversed but the naming conventions stay the same as those used for discharging.