The parsec is a unit of length and is used in the Astronomical system of units. It is denoted by the symbol pc.
It is equal to 3.26156 ly (light years) which is approximately 31 trillion kilometres (19 trillion miles). It's used to measure huge distances to objects and planets outside of our Solar System.
It was first brought into use by Herbert Hall Turner (a British Astronomer) in 1913 and was invented to use in calculations of astronomical distances to make it easier in calculations using raw data.
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.