Equirectangular projection
Why is this map flat?
This map gives every degree of latitude and longitude the same length on the page, so meridians are straight and the terminator is honest. The cost is size: land near the poles is stretched. The picture says so, in numbers from the drawing.
Straight meridians are the point
A globe is the true shape. A page is not. This page’s job is to show where it is light, and that is a question asked in latitude and longitude. The projection that keeps those lines straight is equirectangular.
The poles are cropped (about 82° N to 62° S) because the top and bottom of a full 2:1 map are the most stretched bands, and no city this site cares about sits in them.
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What that costs
On this drawing, a degree of latitude is the same length everywhere, but a degree of longitude shrinks by cos(latitude) on the real Earth and does not shrink here. At 60° the map is twice as wide as the ground. The page should say that whenever it talks about area.
The terminator solve does not care. It is done in latitude per meridian, then plotted. Stretching the picture does not move the answer.