google maps - Why Haversine formula and Web Mercator give different length between two latlng points?

I am calculating the distance between two points given by latlng. However, Google Maps (i.e., web mercator projection) gives me a longer distance than Haversine formula.

Which is the most accurate measure? I can read in some answer that Haversine formula gives it.

So... Is Google Map lying when telling me distance in meters. e.g., in this webpage? http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/

Edit:

Example: In a small area around (37,0), if I calculate area (width,height), haversine results in (7750m*7753m) while Google results in (9784m*9784m).