Not too sure about New Zealand, but in Australia there are several medical programs. Some medical programs are undergraduate, some are postgraduate, but the postgraduate ones usually still let you get “entry” straight after school, you just have to do a 3 year degree first.
The easiest pathway into medicine is using an ATAR and UCAT (if you want to do med next year sign up for the UCAT asap!), and applications generally go through UAC (and it’s counterparts in other states) and require an interview process. Failing this, one can also get into medicine while at university, through a combination of your GPA/WAM (basically just average marks) and by sitting a test called the GAMSAT.