I knew you knew some German but that was impressive ! I had two years of it in high school but I had to use an online translator to fully understand your response.Anywho, the simplest way I could explain the datum concept is that GPS yields a position on the face of the earth. That position is usually expressed as latitude and longitude. In surveying we use coordinate geometry and expressing points with a northing and easting coordinate. That northing is the y coordinate and easting is the x coordinate in the Cartesian system. The GPS receivers and software that a surveyor uses yields the northing and easting and the z coordinate, which is the elevation, in NJ State Plane coordinates.
In NJ we use the NJ State Plane Coordinate System, which is NAD 83, only when required by the job specs. The system is a grid that covers the State and has built in adjustment for the curvature of the earth. As I said before, we rarely need State Plane for the type of work that we do. The reason we hire an outside firm to burn points for us when we need to is that the physical State and Federal monumentation in a lot of areas is either non-existent or too far from the job to be practical to transfer by conventional traversing.
Here is a graphic from the NGS website. If I had a job in the center of this photo that required NAD 83 and NAVD 88 I'd be calling another surveyor to burn some points for me right next to my job. The red circle is a 5 mile radius. If I don't have monuments within a third of a mile or so, I will have points burned. If I was doing a normal property survey I don't need to be in those coordinate systems and we perform the same work in a random datum that allows us to plot what we did and generate our plans.
