Why do flat maps distort the world?
A flat map can’t show the round Earth without bending it. The US Geological Survey puts it simply: a flat map can keep true directions, true distances, true areas or true shapes, but never all four, so every projection chooses what to keep.
Mercator: true directions, swollen poles
On a Mercator map, the USGS notes, a straight line drawn anywhere is a true direction, which made it the sailor’s map. The cost is size: Mercator draws an area four times too large at 60° north or south and about eight and a half times too large at 70°, so Greenland, northern Canada and Antarctica look far bigger than lands near the equator.
The projection behind most web maps
Map tiles are usually drawn in Web Mercator, a version of Mercator for the web. The USGS uses it for all the tiled base maps of The National Map so they can be combined with other common map viewers. Zoomed out, such maps show the same swollen high latitudes.
Why it hardly matters close up
Distortion grows with the area a map covers. The USGS says a 1:24,000 topographic map drawn on a Transverse Mercator projection is nearly correct in every respect. The maps on this site’s county and town pages cover small areas, so their shapes and distances stay close to true; the world and time-zone maps do not.
Other choices
Equal-area projections keep sizes right but bend shapes; equidistant ones keep distances true only along certain lines, such as those running out from a chosen center. Coordinates are the same whatever the projection: a latitude and longitude name the point, and the projection only decides where it is drawn.