The league is a ancient unit of length that doesn't below to a unit system. Its symbol is simply - league.
It was originally an ancient Celtic unit as well as being common in Latin America and meant the distance "a person could walk in an hour". It is no longer a recognised unit in any nation.
Once it started to be quantified, in Argentina (legua) it represented 5.572 km, in England it was quantified as 3 miles and at sea a league is 3 nautical miles (3.452 miles).
The mile is a unit of length in the imperial unit system with the symbol mi.
It was originally an English unit but was adopted by many countries who all had their own slight variation on definition. The English mile, however, is equal to 63,360 inches, 5280 ft or 1760 yards.
The UK still uses the mile on all roadway signs rather than the kilometre; its SI "equivalent". It used to have the symbol 'm' until SI was established and it was changed to avoid confusion with the unit metre.