My understanding in NSW, as I am going through the process this week.
First up, "mooring apparatus" is what can be brought & sold, that is the weight, chain, ropes, float etc.
You lease a portion of the sea floor from Maritime, so you are correct, you can not buy a "mooring / and its location"
Just buying a boat and mooring apparatus does not guarantee you can keep the boat on that mooring, but if no wait list in the area you can apply to be the new lease holder. A phone call to Maritime / local BSO should answer most of your questions.
You have to do an "application for transfer of a private mooring licence"
Or you can pick the mooring apparatus up and move it.
roads-waterways.transport.nsw.gov.au/maritime/moorings/private-moorings/index.htmlwww.nsw.gov.au/sites/default/files/2021-03/Private-mooring-licence-conditions.pdf