A coordinate system is set of mathematical rules for specifying how coordinates are assigned to points. This is unrelated to the Earth. A coordinate reference system (CRS) is a coordinate system related to the Earth through a datum. Another commonly used adjective for an earth based CRS is georeferenced or non-georeferenced for a Cartesian coordinate system. Colloquially the term coordinate system has historically been used to mean coordinate reference system and this mixed use is sometimes followed here.
Coordinates, the points lines and polygons that make up spatial locations, define a position unambiguously only when the coordinate reference system to which those coordinates are part have been identified. It is a common misconception that Latitude and Longitude alone can locate a position on the earth. Figure 1 below gives an example of the amount of error possible by providing a point without it�s corresponding coordinate system. Which is correct?
Figure 1 Location variation based on different coordinate reference systems assignments
All told, spatial data needs an accurate coordinate reference system. It is the structure or framework that holds the data. One of the greatest pitfalls in making use of spatial data is incorrect or incomplete reference to a well defined coordinate system. A coordinate system locates the data in two-dimensional or three-dimensional space. Knowing the coordinate system is very important if you want to combine data from different sources. Many coordinate systems have well known definitions provided by knowledge standards organizations and agreed to by commercial software vendors. Others are customized by companies and individuals at the project level.