> An example that should be familiar to many software engineers is the taxicab metric, also known as the Manhattan distance. ... There are some unnamed geometries in between, but if n approaches infinity, we get what’s called the Chebyshev distance.

I like to think of these two metrics and "rook" and "queen" distance. Manhattan distance is how far away two points are if you are traversing using a rook in chess which can only move horizontally and vertically. Chebyshev distance is how far they are if you can also move diagonally.