Ok lets all slowwww down. Bonding and grounding are very different and should not be confused.
Grounding, as applies to pools, is connecting all electrical equipment to the service entrance neutral buss bar. Its covered in NEC Article 250 and for pools in NEC Article 680.6. Grounding of pools does not include ground rods.
Generally The NEC requires all electrical components of a pool, the pumps, heater, SWCG, utility plugs, lights, automation systems to be connected back to the service entrance neutral bus bar by an insulated ground wire. No bare copper, no using metal conduit as a equipment ground. Insulated ground wire and only insulated ground wire. The purpose of grounding is to direct a fault current back to its source by a low resistance path in such a manner so as to trip the overcurrent protection device (the circuit breaker) and prevent harm to humans.
Bonding, as it applies to pools, is installed to reduce voltage gradients in the pool area. NEC 680.26(A) In English that means that if any part of the pool structure or equipment does become energized (be it from a local source or a outside source) then the whole pool structure and equipment will be energized. If it's all energized then a human being cannot act as a conductor and does not get shocked no matter the source of the current.
The bonding rules can be complex but in summary a concrete pool must have its rebar shell connected to a copper bonding conductor in 4 different locations and the conductor must be solid #8. The deck or surface outside the pool should hace a rebar or copper cage around the pool extending three feet from the pool. You may use a #8 copper wire around the pool as a substitute in some jurisdictions. The water and all metal parts of anything within five feet of the water must be connected to the bonding loop including the pumps SWG and heater. Even if they are grounded. The bond wire must be connected by screw clamps listed by UL for that purpose.
So hire the second electrician and have him examine what you have and figure out a way to make it work and comply with NEC 680. You may need to chip up some concrete but I'm not there so I can't tell you the best solution.
If you have questions post on this thread. When does the pool open so I can come swim

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