Some people are confused about cathode and anode when studying about chemistry or physics because of the appearance of battery. For the regular alkaline battery we are using for example, we can see that the postitive end is anode, and the negative end is cathode. This is printed on the battery. That means the anode is positively charged, while the cathode is negatively charged.
Now here is the problem. How does the electrons move inside and outside the circuit? Some people thinks that electrons move from anode to cathode. I will say yes, reason is that the electrons move from the anode to the circuit, then from the circuit back to the cathode. This is what we learn in physics. Same thing happens inside the electrolytic cell.The anode is positively charged because cations (which are positively charged) moves to the anode from cathode, and the cathode is negatively charged because anions (which are negatively charged) moves to the cathode from anode.Cations gain electrons and are reduced at cathode, and anions lose electrons and are oxidize at anode. That means inside an electrolytic cell, eletrons move from anode to cathode.
Our conclusion is, elecctrons always move from anode to cathode in a circuit or electrolytic cell.
In chemistry, another important thing to remember is that reduction occurs at cathode, and oxidation happens on anode, as what I mentioned above.