Equirectangular
The naive one: plot longitude as x and latitude as y. Area and shape both distort as sec(latitude), exactly half the exponent of Mercator's.
What it does
It plots longitude as x and latitude as y. There is no mathematics in it at all, which is why people often treat it as "the raw data" rather than a projection. It is a projection, and it has its own trade-off like every other.
Its two distortion axes are the same curve: area and shape both grow as sec(latitude), and both read 9.57 at 84 north. That happens because its meridian scale is fixed at 1, so all the area distortion comes from parallels being stretched - which is also all the shape distortion.
Why it is here
This tool moves shapes by rigid rotation of the sphere rather than by adding a delta to longitude and latitude. The simpler approach was rejected because under Mercator it renders shapes at the wrong ground size (ADR 0003). Under Equirectangular, adding a delta looks right. This map is the one place where the rejected model holds.