People tend to confuse a Rolex Chronograph designation with that of a Rolex Chronometer, however, they are completely different and unrelated.
Definition: Rolex Chronometer is a certification that is given to a watch that has the highest level of precision. The certification is only awarded to automatic or mechanical movement watches.
Any watch that earned the Chronometer Certification had to pass rigorous testing criteria set forth by the Swiss Official Chronometer Control (COSC).
A Rolex chronometer’s mechanical movement is very close to perfection, thus, the time it displays is usually very accurate (unlike other self-winding or automatic watches), and therefore carries a premium over non-chronometer watches.
Fifteen days of testing are conducted by the Swiss Official Chronometer Control (COSC) include testing a watches performance under different temperatures extremes, in different positions, and submerged under-water.
A Chronograph is a watch with stopwatch functions, like the Rolex Daytona, but Rolex does not call the Daytona a Chronograph, they call it a Cosmograph.
A Daytona has multiple counters for measuring elapsed time, counting registered seconds, minutes and hours.
So to conclude: A Rolex Chronometer is a certification of timekeeping accuracy, and a Chronograph or Cosmograph has additional time measuring functions.
To give a few examples of the differences between a Chronometer and Chronograph, Rolex makes a Stainless Submariner without a date with is neither a Chronometer or Chronograph, although the Submariner with the date is is COSC certified.
The Stainless Rolex Daytona is both a Chronometer and Chronograph, but Rolex has its own special name for their Chronograph. They call it a Cosmograph. O.K. my head is spinning...