I've never heard anyone in Australia refer to soccer as 'association football'.
That's the name of the sport.

From
wikipedia:
Association football, commonly shortened as football and named soccer in some locations...
The word "association" in this term refers to the Football Association or the FA, founded in London in 1863, which published the first set of rules for the sport that same year.
It's important to note that this FA is not the same FA as in "Sweet FA" (delicately translated as "Sweet Fanny Adams" or less delicately as "Sweet F*** All"). Warning: do not look at
this article on Fanny Adams if you have a sensitive nature. Seriously.
Anyway: football is, of course, very old and dates back to the time that the victors in a battle used to kick around the heads of the losers for sport (possibly as early as the 8th century CE). In medieval times, football had very few rules and could be played by entire villages against other villages, with the goals being a village border, and anything was allowed to get the ball, including using your fists, boots and even knives. English bishops and kings often complained that football was either ungodly or distracting people from archery practice, and tried to ban it repeatedly, without success.
There were several attempts to codify rules, but the game only became slightly manageable when the Football Association took charge in the 1860s.
