Definitely that, but I would argue difference is not in spite of living next door but because of it. Canadians because they are so similar always want to find a way to show how they are different as since share a common language and culture fairly similar so political values is one of the best ways of being different. Ireland and UK do in some ways have similar parallel, but their Catholic religion and Irish language are big things Ireland uses to show differences not politics. Yes few speak Irish language, but fact mandatory in school and all government signage has Irish and usually first line and larger print goes to this. And unlike in Western Canada where many complain about French being on cereal boxes, no one seems to have a problem with Irish being used to extent it is despite few native speakers left. Religion probably less of a difference although still a huge issue in Northern Ireland as Catholics and Protestants rarely live in same neighbourhoods and attitudes on whether remain in UK or join Republic of Ireland split along this.
Australia and New Zealand are both middle powers so not sure it plays as big a role. Also US is unusually conservative for a Western country whereas Australia and UK are not so as they often say whenever you go too far in one direction, you get an equal and opposite reaction in other direction and in some ways that is what is happening in Canada.
Finally a big one is establishment. In UK, establishment tends to favor Conservatives and I think in Australia much the same while in Canada our establishment often called Laurentian Elite is very much on progressive side and tends to favor big government and wary of more individualistic politics. US establishment like Canada generally leans left although leans more right on fiscal policy but left on social. But since US founded on a revolution unlike Canada, they have a much more anti-establishment culture whereas Canada's much like UK is more pro-establishment. France despite being more left leaning also has strong anti-establishment like US that UK lacks for same reason. Its why you see political riots quite often in France, but in UK it's mostly football riots but almost never political or at least rarely. In UK anti-establishment was Labour Party in many ways while Tories when old PCs were pro-establishment, but Reform party very anti-establishment and it now dominates Tories so Canadian Tories and Labour are both anti-establishment in fairly pro-establishment countries.
So looking at the Wikipedia page for Australia and New Zealand relations, I came across this.
Despite some shared similarities, the cultures of Australia and New Zealand also have their own sets of differences and there are sometimes differences of opinion which some have declared as symptomatic of sibling rivalry.[2] This often centres upon sports[3] and in commercio-economic tensions, such as those arising from the failure of Ansett Australia and those engendered by the formerly long-standing Australian ban on New Zealand apple imports.[4]So from what I can tell, since both were part of the British Empire for a similar amount of time (IE same political system etc), it looks like they differentiate themselves through stuff like this. Almost like 2 U.S states (Packers vs Bears) or 2 Canadian provinces (Leafs vs Habs), with a bit of "Why the American chain Target failed in Canada" thrown in.
In addition to that, the 1901 Australian Constitution included provisions to allow New Zealand to join Australia as its seventh state, but New Zealand chose not to join Australia due to perceptions that the indigenous Māori population would suffer as a result.
So it's different than the U.S and Canada. But similarly to the U.S and Canada, it's the smaller country wanting to assert its independence.
