Geodetic Surveys - are surveys, which take into account the true shape of the earth.
Geodetic surveys are typically carried out with great precision, often over long distances, and are used not only to determine the size, shape and gravity field of the earth (the science of Geodesy ) but also to establish highly accurate Control Networks.
Plane surveys - are the most commonly practised method of surveying and treat the earth as a flat or "plane" surface. Good enough for small-scale surveys in limited areas, the curvature of the earth has no effect on the results, thus the computations and results can be referenced to a plane or flat surface.
Plane surveys are used for the determination of legal boundaries, for engineering surveys for the construction of buildings and roads and for small-scale topographic surveys.
Plane surveys may also be used to establish small control networks for construction sites and subdivisions or for open-pit mines or even to add control, called "densification", to larger Geodetic networks.