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 millimetre is a unit of length in the metric system, equivalent to one thousandth of a metre (the SI base unit of length).