Football is a term for a game that is played on foot because other sports were on horseback at the time. It's not called football because it's played with your feet. Many in Australia, New Zealand and Ireland refer to association football as football, likely to differentiate it from Australian football and Gaelic football, which are commonly referred to as football in those countries. This is not the case in the United States, where American football is simply called football.
The term association football was coined in England by the Football Association in 1863 to differentiate it from other versions of football played at that time, particularly rugby. The rules of association football were codified in England by the Football Association in 1863. This is why association football is the most popular sport in the world, but there is no consensus around the world on what it is called. In Canada, the governing body of the sport is called the Canadian Football Association, although its original name was the Dominion of Canada Football Association. In the United States, a sport emerged at the end of the 19th century that borrowed elements from both rugby and association football. This sport is now known as American football and is referred to simply as football. In most parts of Ulster, especially Northern Ireland, East Donegal and Inishowen, association football is generally referred to as “football”, while Gaelic football is generally referred to as “Gaelic”.
Meanwhile, in countries where there is another major sport called football (e.g. USA), people still refer to association football as “football”. This coincidence is reflected in the auxiliary languages Esperanto and Interlingua, which use “football” and “football” respectively. You will find that many countries refer to association football as “football”, including Australia, New Zealand and Ireland. This is likely because these countries have their own competitive version of football and they use this term to differentiate it from other sports such as Australian football and Gaelic football.
In the English-speaking world, association football is most commonly known as “football” or “football”.