While constructing a map the sphere is projected either directly onto a plane or first onto a auxiliary surface (rotation cylinder resp. rotation cone). Next the auxiliary portrayal surface (cylinder resp. cone) will be unwinded onto the plane. This procedure delivers a main criterion for the classification of map projections according to the type of the (auxiliary) projection surface
All in this way constructed map projections are named true projections. They are also called conical projections, because the plane and the rotation cylinder can be interpreted as a marginal case of a rotation cone:
If you (slice and) unwind a rotation cone onto the plane, a circle sector will be formed with an opening angle k * 2 (0 ≤ k ≤ 1). For k = 1 this circle sector will become a full circle and the cone will change to a plane (left figures) (azimuthal projections). For k = 0 the circle sector will become a strip and the cone will change to a cylinder (approximately right figures) (cylindrical projections).