Short answers, pulled from the story.
The imperial gallon is defined as exactly 4.54609 litres, while the US gallon is defined as exactly 231 cubic inches. The difference arises because the imperial gill divides into five fluid ounces and the US gill divides into four, alongside a slight difference in the sizes of the imperial and US fluid ounces.
Both the US gallon and the imperial gallon divide into four quarts, eight pints, and thirty-two gills. Each quart holds two pints, and each pint divides further into cups and gills.
The wine gallon was redefined as exactly 231 cubic inches in 1706 during the reign of Queen Anne, and it was legally adopted as the standard US gallon in 1836. The figure of 231 cubic inches remains the definition of a gallon in the United States today.
Britain adopted the imperial gallon in 1824 and abolished all other gallons in favour of it. It was redefined by an Order in Council on the 28th of November 1889 and again in 1963, with the exact figure of 4.54609 cubic decimetres adopted in the United Kingdom in 1976.
The imperial gallon is still used to sell petrol in eight Caribbean territories, including Anguilla, the British Virgin Islands, the Cayman Islands, Montserrat, Antigua and Barbuda, Grenada, Saint Lucia, and Saint Vincent and the Grenadines. The US gallon is used to sell gasoline in the United States, Guatemala, Colombia, Ecuador, Peru, Haiti, the Marshall Islands, the Federated States of Micronesia, Palau, and Liberia, plus four US territories.
The EU directive 80/181/EEC removed the gallon from the list of legally defined primary units of measure for trade and official purposes, effective from the 31st of December 1994. The United Kingdom replaced the gallon with the litre as a primary unit effective from the 30th of September 1995, though the gallon can still be used legally as a supplementary unit.
The US dry gallon was defined as one-eighth of a US Winchester bushel of exactly 2150.42 cubic inches, equal to 268.8025 cubic inches. It was used in the United States for grain and other dry commodities until the 1990s and is no longer used or listed in the relevant statute.