A nautical mile is a fixed distance, it is the distance between 1 minute of longitude at the earth's equator. It is also the distance between 1 minute of latitude all over the earth. Nautical miles are used in navigation, because it's far easier to figure out distances in nautical miles than in any other unit when travelling between two points. On land we don't really travel between points or navigate, we just stay on roads for X distance until we arrive. I really don't have any idea why statue miles came into use, but they don't help anyone when navigating, and kilometers help even less, since they are not based on geography at all.
If you want to calculate how far you have flown, you use starting location in Lattitude and Longitude and final Lat. & Long. to determine total distance. You will end up with a distance in nautical miles. If you want it in statute miles, you have to convert from nautical to statue miles.
I know this doesn't really help, but at least you know why knots and nautical miles are used when flying.
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