The light year is a unit of length in the Astronomical system of units. It uses the symbol ly.
Often confused with a unit of time as it contains the word "year", it is actually defined by the International Astronomical Union (IAU) as the amount of distance that light travels in a vacuum in one Julian year (365.25 days).
Using the speed of light (299,792,458 m/s or 'c') and the Julian year (as apposed to the Gregorian year which is 365.2425 days), we can equivalate 1 light year as 9,460,730,472,580,800 metres or ≈ 9.46 trillion kilometres.
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.