'Code' only matches 'style' in this context. There are many games around the world called 'football' and these different types are called 'codes'.
Association football is a code of football. This is the one Americans refer to as 'soccer' (but it's also called 'soccer' in other places too).
Other codes include:
Rugby football (union and league)
American football
Australian rules football
The dominant code in any region is always just referred to as 'football'.