I have been learning Transformation concepts working with matrix algebra to develop a basic 2d conformal transformation calculator in excel. The scale is developed as a relationship between line segment lengths between one coordinate system and another. But my question is concerning the concept of scale as it relates to a survey perspective that scale in a transformation is used to change between grid and ground. It is my understanding that the two scales are different; one derived from a line segment length ration, and the other based on the earth radius, resulting in two different scales and two different processes that use these scales. I wonder if someone can confirm my understanding above, or if a reference could be recommended that may explain the differences between the two scales.