Ok, I believe I understand a lot of what 250 is saying after reviewing it. I would like to share my understanding so that anything can be corrected if I am wrong:
Main bonding jumper - Connection point in the form of a green screw in a busbar inside the service enclosure connection making common: earth (grounding electrode conductor), utility neutral, and equipment grounding conductor OR supply side bonding jumper (if applicable).
System bonding jumper - connection point of all of the above with the exception of utility neutral being replaced by the generator/solar/other separately derived system neutral conductor.
(Where both a separately derived system and a utility system exist, only one neutral to case bond would be required at the utility/main service equipment IF a transfer switch was in place with the neutral NOT being switched between the two, else, both a system bonding jumper and main bonding jumper would be installed.)
Grounding electrode conductor- wire ran to grounding electrode system such as metal water pipe, ground rods, rebar, structural metal to main bonding jumper connection only (never supply side bonding jumper)
Supply side bonding jumper - grounding conductor between service equipment and service disconnecting means (where in separate enclosures). Neutral to ground connection already established upstream.
Equipment grounding conductor - ground wires or conduits for branch circuits and feeders 250.122
Equipment bonding jumper - Conductors connecting metal parts of boxes/enclosures together. Can be bonding locknut, bonding bushings with ground wire where applicable.
Equipment grounding conductors never have to be larger than ungrounded conductors for the circuits they serve.
Largest overcurrent protection determines equipment grounding conductor size where multiple circuits ran in same raceway.
Where the equipment grounding electrode system has multiple electrodes present, all shall be bonded together. Where none exist and you decide to drive ground rods, one rod + one supplemental rod must be installed no less than 6 ft. apart.
Where only a metal water pipe exists, any supplemental electrode shall be installed and bonded together.
Metal water pipes are permitted to be used as a connection point of multiple grounding electrodes as long as the mechanical device is accessible.
Supplemental electrodes shall not be required to be bonded with larger than 6awg copper, and the main grounding electrode shall be sized based on 250.66.
I know that is just the tip of the iceberg but I want to make sure I'm understanding it correctly.....