Picture a with several desks, each one covering a patch of the world, and one editor in charge of each patch. City editor names the editor whose patch is called the city. The whole difference between the two meanings is which city the means. In an American paper it means our own town, so the patch is local news. In a British paper it means the City of London, the square mile of banks, so the patch is money.
From the word’s history
Wiktionary's UK entry says the City editor covers affairs in the City of London, the UK's main financial centre, and by extension business and finance in general. That is the route from a place name to a subject area.
Wiktionary 的英式條目寫得很清楚：City editor 負責的是倫敦金融城（the City of London，英國主要金融中心）的消息，再由此延伸到整個商業與財經。也就是說，那條路線是從一個地名，擴大成一個報導領域。
Wiktionary, "city editor"
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