At first glance, they appear to be the same thing but examine the detail and there, you will find, lurks the devil. Whilst there is plenty of online information to define both, there is little to explain why this seeming duplication exits.
I hope to shed some light here, though (disclaimer alert), my observations are subject to some conjecture because the 'why' factors are not necessarily clearly stated.
First to set the scene. Australia has a federal political system, i.e. a national government for some functions and state governments for others. There is plenty of overlap and this is never more apparent than in health.
Public hospitals and community services are funded by the states, and private health is heavily supplemented through Medicare which is governed by the federal Department of Health and Ageing. Cost for healthcare falls to one or other jurisdiction depending on where it is delivered, and by whom.
Doctors are, of course, expensive to hire and generate even more cost through their practice. Both layers of government, therefore, want a say in controlling the appointment of doctors in 'at need' positions in order to manage cost as it impacts their own budget - hence the duplication.
DWS is a federal mechanism to control cost through billing activity by restricting the number of Medicare Provider Numbers issued, for a particular specialty, in a particular geographical region.
AON is a state control on the appointment of doctors, mainly onto their payroll and into their state run facilities with the attendant costs that this will incur.
Cost, of course, is not the only consideration. Both branches of government are motivated by the communities need for healthcare services, but money inevitably informs their philosophical and practical approach to the issue.
You will unavoidably have to go through a lot of duplicated paperwork.
So there you have it. It may seem illogical at first but the system has evolved as it has for an explicable reason.
Is there room to improve the system? Absolutely, it could be streamlined with greater coordination and less double-up - but that's another topic.
On balance I think that the process and paperwork to get into Australia is generally reasonable and fair (try getting into Canada as a specialist!) so there is little point in complaining. You might as well just get on with it.
Just try to remember that it will all be worth it in the end.
Written by Dr John Bethell, Director of Wavelength International