What sport does the word 'football' belong to?

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Football is a common name for a lot of sports, however what sport shold be called football? In Amrica, Australia and Canada etc, they call American football, football. But in Britain and other place in the world football is what Americans call 'soccer'. Football was made decades ago, and American football is a newer sport compared to Football(soccer). So if this is the case what sport should carry the name 'Football'