We mentioned storing electricity in a battery. A battery stores energy electrochemically, meaning that electrons are “stored” in a chemical with high energy. Any chemistry that involves electrons as reactants and products is electrochemistry. A fuel cell is similar to a battery: both have two electrodes (anode and cathode) and an electrolyte.
There is more than one way to distinguish a battery and a fuel cell:
Batteries store their chemicals inside the battery, while fuel cells are fed from outside. 
Fuel cells often involve catalysis, while batteries may not.
Fuel cells operate continuously. Batteries operate in a batch manner, i.e. charge/discharge.

We mentioned storing electricity in a battery. A battery stores energy electrochemically, meaning that electrons are “stored” in a chemical with high energy. Any chemistry that involves electrons as reactants and products is electrochemistry. A fuel cell is similar to a battery: both have two electrodes (anode and cathode) and an electrolyte.

There is more than one way to distinguish a battery and a fuel cell:

  1. Batteries store their chemicals inside the battery, while fuel cells are fed from outside. 
  2. Fuel cells often involve catalysis, while batteries may not.
  3. Fuel cells operate continuously. Batteries operate in a batch manner, i.e. charge/discharge.