Bonding and grounding are often confusing subjects, and are not the same.

Bonding refers to connecting items together. All metal objects which can come into contact with pool water should be bonded together. This prevents any one of them from becoming a different potential from any other, from whatever influence, direct electrical contact, induced current, chemical, etc. This bonding prevents any current flow through the water itself, thereby protecting the occupants.

Grounding, on the other hand, indicates a connection of one or more components to the service ground, equipment ground, ground rod, or other ground-potential reference point. Technically, there should only be one ground reference in an electrical installation, and that is most often at the service feed point. Everything else which is to be grounded should tie directly to that point with minimum resistance.

Technically, in a grounded system, bonding is simply a means of connecting the ground wires to everything. In an ungrounded system, a bond wire just connects it all.

There is also much debate over whether or not a bonded pool grid is to be grounded, and as I understand it, there are differing local code requirements as well. Some say ground, some say isolate. I'm personally a "ground it" fan.

As an aside, the GFCI protected circuit does not need a ground connection to the GFCI to be protected. GFCI devices are designed to measure differential currents between the hot and neutral conductors, and open the circuit if that difference exceeds the trigger, around 5 milliamps. It is assumed that any difference in current is being diverted out-of-circuit by a body somewhere. Naturally, a ground is required by the circuit according to code, but it is not necessary for the GFCI feature to function.