Any kind of projection of a sphere on a plane surface is distored. There are different kinds of distortions : conformal distorsion (which ensures angle conservation), equivalent distorsion (which ensures area conservation) and compromise distorsion. The compromise distorsion is a mix of the conformal and equivalent distorsions, and therefore alters both the angles and areas but reduces overall distorsion. The equidistant projection is a compromise distorsion for example.

The Robinson projection is a compromise projection :

(Source : Wikipedia)

Voir : Projection (System of)
(French : Aphylactique (Projection)]