A few points, first, about vocabulary.
A "Ufer" is a ground that utilises the rebar in a concrete slab as the grounding electrode. It is typically made, at the time the slab is made, by attaching 20 ft. of #4 to the rebar at multiple points.
A "concrete encased electrode" is typically a 10 ft ground rod, with the top two feet bent at a 90 to the body of the rod. The rod is laid in a two foot deep tranch, and surrounded by twominches of concrete.
The "ground rod" or "grounding electrode" is there to give lightning somewhere to go. On older homes, sometimes a water supply main was used for this purpose, but that practice has ended with the advent of plastic pipe. Today, with a "service change," we end up installing a grounding electrode of some sort.
Another matter is "bonding;" that is, tying to the ground system anything that might become "live" should something go wrong. We "bond" the water pipes, gas pipes, and many other things to the bybtem, typically by running a #8 wire from the item to the ground buss at a panel.