What is the difference between a Rolex Chronograph and a Rolex Chronometer?

Rolex Daytona is both a Chronograph and Chronometer

Launched in 1963, the Rolex Daytona contains the Chronograph features such as the stopwatch functionality typically used in the racing industries.  Modern Daytona Chronographs have three additional subdials (also called registers) on the face of the timepiece.  These subdials are controlled by the two pushers on the right side of the watch, above and below the winding crown.  These pushers allow the racecar driver to accurately time the speed attained during a lap and the amount of time it takes to travel the whole course.  This can also be used in other active sports.

Rolex often rebrands certain things, as they have done in the photo above.  Instead of their Daytona, only being a chronograph, Rolex dubbed it a "Cosmograph."  Certainly there is a marketing element to it.  However, since the Daytona is both a Chronograph and a superlative Chronometer, I would say that the excitement leading to giving their Daytona a new nickname, is well deserved.

The Superlative Chronometer for a Rolex timepiece is quite different from a Chronograph/Cosmograph.  It indicates that the timepiece has been assembled with extreme care and tested to ensure that the watch meets the most rigid precision standards. 

Watches that are given the "Superlative Chronometer" label have been certified by the COSC, the Official Swiss Chronometer Testing Institute.  It tests the accuracy of the movement for 15 days and under various conditions.  The time must be accurate to between -4 and +6 in order to pass the test.

As if not to be undone, the Rolex Marketing Machine also awards its chronometers with the Green Rolex Seal, which is boxed with all new chronometers. Again, I don't hold it against them.  The thrill of handcrafting each Rolex masterpiece is worth an extra award.  So, why not a green seal of approval?