Since a globe cannot be peeled off and laid out flat, world maps are always a compromise. Only a projection of the globe. There are three ways of constructing a projection of a globe.
Some projections preserve both distances and directions from a single given point.
Such a projection is called 'equidistant'. There are also projections which preserve directions at any point on the globe. Such projections are called conformal. Finally, there are projections which preserve area sizes, and they are called 'equal area'. There are also many projections that have none of these three qualities.