NSW reopening on Oct 11, page-58

"Both vaccinated and unvaccinated can catch and spread the virus......why is there a vaccine passport?"

because one has greater odds of contracting and hence spreading.
Medical studies proving this have been posted many times

"The incidence of SARS-CoV-2 infection, hospitalization, and death is higher in unvaccinated than vaccinated persons, and the incidence rate ratios are related to vaccine effectiveness."

https://www.cdc.gov/mmwr/volumes/70/wr/mm7037e1.htm?s_cid=mm7037e1_w