Galvanic versus electrolytic cells
Both galvanic and electrolytic cells couple oxidation and reduction reactions through electrodes and an electrolyte, but they run in opposite directions. A galvanic cell, also called a voltaic cell, uses a spontaneous redox reaction to generate an electric current; this is how batteries work. An electrolytic cell does the reverse, using an external voltage to force a non-spontaneous reaction, as in electroplating or the electrolysis of water.
In a galvanic cell chemical energy becomes electrical energy. In an electrolytic cell electrical energy is consumed to drive chemistry uphill.
Electrodes, signs, and reading the diagram
In every electrochemical cell, oxidation occurs at the anode and reduction at the cathode. The polarity of those electrodes, however, flips between cell types. In a galvanic cell the anode is negative and the cathode positive, since the reaction pushes electrons out spontaneously. In an electrolytic cell the external power source makes the anode positive and the cathode negative.
Tracking the sign of the cell potential clarifies the difference: a positive cell potential indicates a spontaneous galvanic reaction, while a negative one means an external source is needed, defining an electrolytic process.