Distances in Voronoi
In a nutshell:
The 4 different methods to calculate the distance between two points are:
where X stands for the (absolute) difference in the x coordinates and Y for the (absolute) difference between the y coordinates. And the n in the Minkowski distance is the exponent in Blender.
F1 calculates the distance between two neighboring points and F2 between one point and the one 'next to the neighbor'...
See also here: https://cgcookie.com/questions/11248voronoidemystified

spikeyxxx
Erratum:
The correct form of the Minkowski distance should (of course) be: the nth root of the term between brackets!
And accordingly the other distances (the Euclidean distance is the square root of (X² + Y²), and so on...).
This logically extends to 3 dimensional distances as you would expect (the square root of (X² + Y² + Z²), etc.)
This is only important if you actually want to calculate those distances; the maiin thing I wanted to show is, that those mysterious names that 'noone' can pronounce, just mean various ways to calculate distances and that there is a simple connection between them...which the above image shows pretty well, I think, although technically not correct...

Great note for those curious!