A chronograph is a timepiece containing two independent measuring systems: one tells the time, the other records short times. Second, minute and hour counters can be started and stopped on demand to directly measure the precise duration of a phenomenon.
A chronometer is a watch whose movement has been tested for accuracy by an official timing bureau. The demands are very high: only a few seconds of variation per day under the most difficult temperature and position conditions normally encountered.
A complication is an additional indication which differs from the simple timekeeping function. The chronograph, striking-mechanisms, repeaters, perpetual calendars, phases of the moon and multiple time-zones are all examples of complications.