Projections and datums definitions

Definitions
 
Coordinate reference system
Set of mathematical rules for specifying how coordinates are to be assigned to points that are related to the real world by a datum.
 
Datum
Parameter or set of parameters that define the position of the origin, the scale, and the orientation of a coordinate system
 
Easting (E)
Distance in a coordinate system, eastwards (positive) and westwards (negative) from a north-south reference line.
 
Ellipsoid
Surface formed by the rotation of an ellipse about a main axis.
 
Geodetic coordinate system
Coordinate system in which position is specified by geodetic latitude, geodetic longitude and (in the three-dimensional case) ellipsoidal height.
 
Geodetic datum
Datum describing the relationship of a coordinate system to the Earth.  A set of constants specifying the coordinate system used for geodetic control. A complete geodetic datum provides, as a minimum, definition for orientation, scale and dimensions for the reference ellipsoid. The concept is generally expanded to include the published coordinates of control stations within the system. 
 
Map projection
Coordinate conversion from a geodetic/ellipsoidal coordinate system to a plane.
 
Northing (N)
Distance in a coordinate system, northwards (positive) or southwards (negative) from an east-west reference line
 
Projected coordinate system
Two-dimensional coordinate system resulting from a map projection.
 
Southing (x)
Distance in a coordinate system, southwards (positive) and northwards (negative) from an east-west reference line.
 
Vertical datum
Datum describing the relation of gravity-related heights to the earth. In most cases the vertical datum will be related to a defined mean sea level. Ellipsoidal heights are treated as related to a three-dimensional ellipsoidal coordinate system referenced to a geodetic datum.
 
Westing (y)
Distance in a coordinate system, westwards (positive) and eastwards (negative) from a north-south reference line.