A geographic coordinate (latitude, longitude and ellipsoidal height) is in terms of a geodetic datum (eg NZGD2000, NZGD1949). The two main ways to transform geographic coordinates between geodetic datums - use a transformation grid or a similarity transformation - are shown in the diagram below.
Similarity transformations (3 or 7 parameter) are performed on Cartesian ( X , Y , Z ) coordinates. This transformation is a three-step process because the geographic coordinates first needs to be changed to a Cartesian value, converted between datums and then changed back to a geographic coordinate.
Additional information and examples of specific transformations is provided in the pages described below.