Some years ago I got involved in a project where it was necessary to calculate the great circle distance between any 2 airports. There were 5 companies involved; the airline and 4 suppliers and the nature of what was going on meant we all had to get the same answer for any 2 points. On the first run none of the results were the same! Some of the differences were minimal (1 mile) but some were in 10s 20s and 30s which could be critical. We never got complete agreement but we reduced the error rate to an acceptable level.
Some of the difference depended on where you measured from/to - the airline hadn't specified so if you measured from the control towers or the end of the runway (which one?) or.... But the main difference came from which model of the earth you use. We tend to think of earth as a perfect sphere even though we know it isn't. A quick Google can take you here :
Javascript Great Circle Calculator - take a look at the dropdown "Earth Model".
I still don't really understand why and it doesn't make any difference to the OP - just a thread drift!