An electrochemical cell is a device that converts chemical energy into electrical energy or vice versa, when a chemical reaction is occurring in the cell. Typically, it consists of two metal electrodes immersed into an aqueous solution (electrolyte ) with electrode reactions occurring at the electrode-solution surfaces. Also known colloquially as a battery. When the cell is connected into a suitable circuit it produces a current and delivers energy. In some cells the chemical reactions can be reversed by using another, stronger, source of emf to drive current backwards through the cell and put energy back. (See charging.) An example of such a reversible battery is the 12 V car battery which consists of six 2 V lead-acid cells.

Check out this website to see a nice diagram of an electrochemical cell:

electrochemical cell

Electrolysis is the decomposition of a chemical compound in solution into ions by the action of passing an electric current through the solution. In other words, the production of chemical energy by passing an electric current through a liquid. This process breaks a chemical compound down into its elements by passing a direct current through it. Electrolysis of water, for example, produces hydrogen and oxygen. Electrolysis is not an equilibrium process; in fact, it is intentionally driven far from equilibrium to cause as much breakdown of the compound as possible. In electrolysis, some atoms are oxidized, while others are reduced.