What is a US league?
A US league is three miles or 15,840 feet. The word comes from the Late Latin leuca, a Gaulish measure traditionally taken as an hour's walk.
The league was used for the distance between towns and for a ship's run at sea. The mile and the kilometer replaced it, and it now mostly turns up in older books. A US league of three miles is about 4.83km.
What is a furlong?
A furlong is 220 yards or 660 feet, which is exactly 201.168 meters. It is an eighth of a mile.
The origin of the term "furlong" can be traced back to Old English, where "furh" meant "furrow" and "lang" meant "long." This reflects the historical use of furlongs in measuring the length of a furrow in agricultural fields. In horse racing, furlongs are used to measure the distance between the starting point and the finish line. A racecourse typically consists of multiple furlongs, with the most common distances being 5 furlongs (5/8 of a mile) and 8 furlongs (1 mile).
Outside the racecourse the furlong has almost gone. British racing still gives distances in miles and furlongs, so a mile and a quarter is written 1m 2f. Road signs don't use it – they give miles and, for short distances, yards.