Australian/NZ Residence Permit

Hi all, maybe a silly question but I can't seem to easily find information either on this forum or google.
I'm trying to work out if there is an actual Residence Permit card that get's issue to prove residency in either NZ or Australia? If not, what is available, whether in the passport or not?
Question is for both permanent and temporary residents.
Thanks very much for your help!

From my Google search of images, it appears that temporary visas (entry clearance) and permanent residence are vignettes are placed in foreign passports for both Australia and New Zealand.