Third rail confusion

That is also my understanding. If you look on the Richmond-Gunnerbury section or North of Queens Park you will actually see the Neg 4th rail bonded to the running rails.

In both 3rd and 4th rail systems, ONE running rail is known as the continuous rail and is bonded to earth. The other running rail carries the track circuit voltage (where these are still used). In places, on the underground the compressed air main pipe is also recognised as earth.

The two rail type is what we have here in Singapore, funny boxes with big cables between two rails abound.

London Underground Earth is a tricky subject, in theory all earths (yes there are more than one) are bonded together but one can still find a PD of 600v between one earth and another !

LUL Traction and signalling supplies are earth free at source and bonded to earth for fault reference purposes.
The +420 & -210 traction voltages are purely arbitrary, being fixed by connecting each traction rail to the continuous rail via some large resistors in each main feeding section (i.e. a number of current sections.
The reference to earth allows earth faults on either traction rail to be detected and a single earth fault will thus have no real effect on the voltage supplied to trains, an earth fault on both traction rails should in theory be enough to trip the traction CBs at the feeding substations but it isn't always the case.
Similarly the 600v ac signal main is earth free such that an earth fault on one leg will not kill the supply but earth faults on both legs have a habit of not only tripping the CBs but also damaging the cable in the process. There used to be an earth reference for the ac main which took the form of three bulbs in series on each leg to earth such that an earth fault would be indicated by three lamps going out and the other three glowing at full brightness. Such lamps were generally installed in call linemens depots but were removed some years ago, the safety elf didn't like them.
Signal 100v supplies are deliberately tied to earth to create feed (BX100) and return (NX100) and an earth reference is important in that earth faults cause failures which are more easily detected than would otherwise be the case.

The continous rail isn't necessarily continuous but where there is one it is bonded around sections which are not part of it and in the tube tunnels it is bonded to the cast iron tunnel segments.

Then there is the fault screen as used on the Victoria line and elsewhere where all the feed and return wires are screened, the screens bonded to a solid copper conductor which itself is earthed.
This tends to cause the feed and return to appear balanced at 50v ac to earth each leg.

Years ago there were multiple earths to be found and that is still the case, for instance Heathrow Express (HEX) necessitated the creation of isolations to create separate zones such that a HEX earth fault would not compromise LUL equipment. Wherever LUL and NR are in close proximity there are generally some special precautions in place to mitigate earth faults from NR overheads. The District line is a case in point as was the H&C between Kings Cross and Liverpool Street.

There are so many issues with earthing, it affects everything on the railway one way or another. For instance LULs MD110 telephone systems had all sorts of transmission timing issues due to earths at different exchanges being at different potentials, CCTV images being obscured by loss of vertical hold due to hum bars created by having cameras connected to earths in different places on a station. The answers to these problems involved careful circuit wiring and isolation to ensure that all the affected equipment was in its own localised system earth zone in much the same way that this is achieved in a simple domestic equipotential zone.

Further to previous postings the "spider" referred to by Roy is actually called an impedance bond. Mostly seen on the Southern and pairs connected by a metal plate enable the dc traction current to flow through but impede the passage of ac track circuit current and both rails have insulated block joints. At points and crossings a single impedance bond is used to bond to one rail on both ends of the point work. When the DC line was converted from 4th rail to 3rd rail traction in 1970, the insulated joints were removed from the running rail adjacent to the +ve conductor rail to form single rail track circuits. Where the Bakerloo operated the centre rail was retained and simply bonded to the continuous running rail. The short circuiting bar in use on the DC lines is fairly short and only reaches between the +ve conductor rail and the adjacent running rail, the problem occurs in points and crossings in that it not always possible to have the return rail adjacent to the +ve conductor rail and then previously guard boards were placed against the conductor rail to prevent the use of the short circuiting bar now a yellow plastic marker is used but this does not prevent the bar being placed on the rail and the resultant mass of burnt track circuit cable and equipment.