Exact, more exact - chronometer. A chronometer is a watch whose precision has been officially tested and certified by an independent testing laboratory. This Certina model has been tested by the Contrôle officiel suisse des chronomètres (COSC), the official Swiss testing authority, and awarded the quality certificate.
The moon phase display is a rotating disc that displays the age of the moon through an aperture in the dial. It can be set by referring to a current lunar calendar. A complex complication, and unquestionably one of the most attractive displays.