Depending on which metric property the projection preserves, we can classify them as follows:

• Conformal: preserving local topography, ie. the shape of features. Examples include Mercator, Lambert Conformal Conic.
• Equal-area: preserving area measure, mostly distorting shapes in order to do that.
• Equidistant: preserving distance between two points.
• Compromise: these provide a representation of the earth that is not perfectly correct in any way but not badly distorted in any way either.