There's a fundamental difference between positions (which might or might not include an orientation) and transformations which can be applied to a position to get another position. Transformations have a group structure (they can be composed with one another to get another transformation), in common cases even a vector space structure (e.g. typical 4*4 matrices) while positions don't have useful operations giving other positions (finding the transform which maps one to the other or finding their distance give values of other types).

Even if you represent positions and transformations in an apparently similar way (for example x,y and z coordinates for points in a 3D space and displacement along three coordinate axes for translations) pretending they are the same thing causes only confusion.