In the republic debate, Australia is not truly debating its independence from Britain. It's not an argument we're having over the influence of the once-mighty master; it's a struggle over our own identity.
The debate about the extent of Australia's alliance commitments with the US, however, is about Australia's sovereignty.
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Obama: US and Australia fight terrorism together
New ways to fight against terrorism will be discussed by President Barack Obama and Prime Minister Malcolm Turnbull during his current visit to the US.
Australian leaders have had some trouble getting the right degree of closeness with the great and powerful friend. John Howard was too deferential in accepting the US misjudgment to invade Iraq; Mark Latham was too angry in rejecting it.
Howard didn't turn Australia into America's "deputy sheriff," but to most of the world it certainly looked like it. Mark Latham's proposal to withdraw Australian troops from Iraq was not mad, but when he described the Howard government as a "conga line of suck holes" he certainly sounded mad.
Latham was dismissed by the Australian people, partly because he seemed too antagonistic to the US ally. One of the conclusions drawn by Australia's political class? It's safer to err on the side of being too close to the Americans than to be too distant.
The former prime minister Malcolm Fraser went further than any other mainstream Australian political figure in seeking to distance Australia from the US. He proposed that Canberra simply cancel the alliance. He argued in his 2014 book Dangerous Allies that Australia is "a compliant partner, a strategic captive of the US". Fraser, who died last year, went so far as to say that Australia had lost the capacity to make its own sovereign decisions.
Even as he wrote, the Rudd and Gillard Labor governments manoeuvred Australia into an ever-closer embrace with the US, persuading Barack Obama to deploy marines near Darwin.
Tony Abbott was disdainful of some parts of the Obama program, notably his commitment to act on climate change. But on the military elements, the hard core of the alliance, Abbott was hard core.
Indeed, he was more gung ho to fight the so-called Islamic State than the US president himself. Abbott committed Australia's air force to fly missions in Syria partly to stiffen Obama's spine.
So now that Malcolm Turnbull had made his first prime ministerial visit to Washington, how is he positioning the alliance?
The early consensus in Australia is that Turnbull has stepped back a little from the great and powerful friend, striking a more independent pose. But is it real?
The early impression in Australian commentary is based on two developments. First was Turnbull's reaction when the US president phoned him last year to press him for trade concessions.
As the US-led Trans-Pacific Partnership agreement was taking its final form, Obama told Turnbull that the US needed a vital Australian concession to bring the 12-nation accord to a happy conclusion.
Australia protects the patent rights of pharmaceutical companies for five years in the Pharmaceutical Benefits Scheme.
After five years, the PBS admits cheaper, generic drugs. Obama said that this to be extended to 12 years or the US Congress would refuse to ratify the TPP. Turnbull said no.
Second was the news that the US had asked Australia for a bigger military contribution to the fight against Islamic State, more usefully labelled Daesh, in Iraq. And that Turnbull's Australia had said no, according to some of the reporting.
There is a problem with each of these apparent acts of defiance. On the trade demand, the problem is that Turnbull's decision was not uniquely a Turnbull decision.
Australia under the Abbott government was shaping to give exactly the same response. Even if an Australian government wanted to yield to the US drug companies, it wouldn't be able to. Because to change the PBS, the Australian Senate would have to legislate. And it's unimaginable that it would.
Australian governments have always resisted US pressure on the PBS. John Howard did. So did Julia Gillard. Abbott was in the process, through his trade minister, Andrew Robb, of resisting too. Turnbull was simply holding the line.
On the demand for more military contributions, the problem is that Australia wasn't specifically asked. The US sent a form letter to all of the 60 countries co-operating against Daesh and asked what they might offer to step up the fight.
Australia, already supplying more military effort than any country other than the US, was not the target. There was no real US request for Turnbull to rebuff. As Obama and top US officials made very plain during Turnbull's visit, the US could not be happier with the Australian contribution.
The impression that Australia was defying the US was based on misinterpretation and misreporting.
As a US expert on foreign affairs Mike Green, former top Asia adviser in George W. Bush's White House, put it: "You don't do form letters to allies, certainly not to an ally who's uniquely committed to the fight."
Green says that US audiences certainly didn't get any impression that Australia under Turnbull was stepping back from the alliance. On the contrary: "His speech managed to impress people with his commitment to the alliance," especially in standing firm on China.
Green congratulates Turnbull for successfully targeting two separate audiences with two impressions: "He managed to find a way to show Australians that he's robustly independent in ways that went below the radar here in Washington."
By giving Australian audiences one impression and Americans quite a different one, "you just have to admire Turnbull's professionalism", says Allan Gyngell, formerly Paul Keating's foreign affairs adviser and now at ANU.
Turnbull has assured the US of a strong alliance, yet given Australians the impression that he has asserted greater sovereign independence. All at the same time.
Peter Hartcher is international editor.