I thought it was explained that bonding is not grounding, though it includes a connection to ground.
Bonding is simply the process of commoning the electrical earths of all the items together via a dedicated lead.
Pumps/heaters etc are all normally earthed via your GPO. Bonding just ensures that all the equipment is at the same common earth/ground which ensures
no potential difference can exist between these items as they are all tied together.
So far so good.
Now to our pools - Pools are not an electrical appliance which is plugged into a GPO so pools natively do not have any direct connection to the electrical earth of your GPO which is where your electrical items get their earthing from.
So there exists the common situation that the pool will be at a different earth potential (voltage) than the GPO earth. Now since all our pumps etc are plugged into the GPO we can normally always measure a difference in potential between the GPO's earth and the pool itself which is a form of electrical ground from an electrical circuit perspective. The reason for this is that ground or earth is only at earth potential at the point where say a ground rod is driven into earth itself - Moving away from this rod will always see a potential difference increase simply because of natural and non natural earth currents and lots of free electrons....!
The pool itself (Gunite only) is a form of ground as it is connected directly to ground via conductive construction components - The concrete, the rebar etc all are actually slightly conductive especially if wet/moist and this is carried right through to the water itself.
From an electrical circuit perspective a fibreglass pool is a slightly different proposition as the fibreglass is an electrical insulator so the water in the pool is totally insulated from any earth (
providing there are no other conductive items connecting the water to any outside components).
Current cannot flow to or from the water in a fibreglass pool unless a conductive device is attached to the pool's water which completes the circuit to outside of the pool.
With a gunite pool current can always flow as the pool itself is electrically conductive to the outside world due to its construction materials which are electrically conductive. So in this instance an electrical pathway is always present for current to flow via the water to and from the outer ground.
This is why it is very important to ensure that the external rebar etc is correctly bonded in a gunite installation as the water is always electrically making contact to the outer shell whereas on fibreglass it is not - it is normally insulated from the external material.
The OP's issue is slightly different again as it is to do with the way the chlorinator operates with it's internal switched mode power supply.
My testing above just verified the OP's issue as I have the same chlorinator.
Switchmode supplies normally have protection and noise suppression capacitors on the incoming active/hot and neutral lines, these allow a small amount of leakage current through and I fairly certain this is what we are seeing.
When the OP and myself unplug the chlorinator there is no voltage between the pool water and earth as it is the chlorinator which is introducing the minor current path via its circuitry.
You will actually receive a much larger shock simply by placing your tongue across a standard 9v battery...
Have you ever used one of those small electrical testing screwdrivers which you place a finger over the end and touch the screw driver tip on the mains and if hot the small neon lamp lights up inside the body of the screwdriver?
If you stand barefoot on concrete or a tiled surface you will feel a tingle at the end of the screwdriver when the neon lamp lights up as current is flowing through your body and through the neon lamp and a resistor. Only a small current flow but you can actually feel it. This current is way higher than what the OP experienced as you can feel the current as the neon lights up through unbroken skin whereas the OP's issue was with broken skin which has way lower resistance.
The chlorinator's power supply will more than likely have a slight leakage current through the capacitors I mentioned - this is normal for these types of power supplies. The capacitors limit the AC current due to their impeadance at 50/60Hz and therefore the current cannot get any larger etc. This does not mean that the pool is electrically un-safe or that the chlorinator is faulty.