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Nautical miles measure distance. 1 nautical mile is the angular distance of 1 minute of arc on the earth's surface. As these differ slightly (6108' at pole c.f. 6046' at equator) 6080 was adopted (this being it's approximate value in the English Channel). The International nautical mile is 1852 metres, so is very slightly different from the UK nautical mile.
The parsec is a unit of length equivalent to around 20 trillion (20,000,000,000,000) miles, 31 trillion kilometres, or 206,264 times the distance from the earth to the sun.
A parsec is also equivalent to approximately 3.26 light years (the journey distance if you travelled at the speed of light for three years and three months).