I am using ArcMap 10.4.1.
I am looking for confirmation of my understanding of the below scenario. I am trying to understand what happens when two different coordinate systems do not align. The concept appears simple but want to confirm that I am not missing something. I have attached an image of the Lambert Conic Conformal projection model showing the Grid Origin and the Geodetic Origin, as an example. It is my understanding that the grid origin (red X) would correspond to the cad/Esri program 0,0,0 (origin of northing-easting values). While the geodetic origin corresponds to the projected ellipsoid origin, centered on the map (red square). It appears that coordinate systems with different ellipsoids and units would shift the map false northing/easting to a different location, causing data to misalign. By toggling the coordinate system alone is not enough to change the map data, but by performing a transformation-projection on the data allows the software to read the northing-easting coordinate values relative to the false northing/easting of the ellipsoid that is active in coordinate definition.
Does the above concept sound correct or could there be more to this concept that I am not aware?