"Publish" is like completing the SPFR report. It won't go to ATO or any third party. It is mainly for reporting purposes.

"Published" is the same as "Lodged", once you press Publish, no further changes on that set of accounts can be made. To make a change, it's necessary to start from scratch & build a new set of financials for the same timeframe.

Below examples show that "Draft" SPFR can be deleted (with an "x" button), but the "Published' SPFR cannot be deleted, also you may find below the duplicate year 2020/2021 SPFR