I could be wrong here so don’t quote me …
Play group is just a get together of families, maybe everyone brings a plate to share, it’s freestyle so you just turn up and hang out.
Playcentre is more structured learning, I think they have to have at least 1 qualified early learning teacher in attendance. I also think it’s more involved so the parents are setting up activities and are expected to help fundraise, run sessions, clean up, maintain the property, etc.
Playgroup is more fun, playcentre is more structured.