New Australian Passports Allow Third Gender Option

Australia's new passport has a section for be who are either transgendered or lack a sex. On this passport, there will be a section marked with an X for these people. The passport's main purpose, according to an Australian senator, will help prevent gender discrimination. This new passport will also prevent classifying for people, since before this passport was created, people were required to have surgery designed to give a person a specific gender depending on which gender they preferred.

Is there a difference between gender and sex? Does a person's chosen gender lead to gender discrimination?