Ideally, these factors would be consistent to the relationships on the real earth. Unfortunately, some relationships are always distorted. Equal area projections preserve the property of area. On an equivalent projection all parts of the earth's surface are shown with the correct area. However latitudinal distances are not accurate.
Conformal projections preserve the property of shape over small areas.
Conformal projections are used because they preserve directions around any given point. Additionally, relationships of the angles within the graticule can be shown correctly. Area and shape are normally distorted. Because of GIS emphasis on area portrayal, GIS systems often use conformal projections. Some projections only preserve correct distance relationships along a few places on the map.