Some people are apt to assert that the rule of thirds is the same as the golden mean. The proportions are close, but not the same. In addition, most of the various golden mean methods emphasize a primary, off-center subject; the rule of thirds does not suggest an order of precedence among subjects. The rule of thirds involves only straight lines, while some golden mean offers the Fibonacci spiral for placement. The rule of thirds offers four points of interest and four division lines for the main elements; the golden mean can be used to proportion elements more deeply embedded in the composition.
In the following image, a 2:3 image, divided in vertical thirds and horizontal thirds, is shown in pink. A frame conforming to the golden ratio is shown in green.
You do not have to use either of these methods to construct your compositions. In four years of art school, not a single instructor or textbook mentioned either of these methods. They are relatively quick and easy ways to begin thinking about composition and the placement of elements. For this reason, many photographers benefit from trying them.
Also see: The Golden Mean
Also see: The Rule of Thirds