Electronic – Driving Avalanche Photodiodes (PCBs)

If you have two separated circuits the voltages of the first don't mean anything to the second and vice versa. If you want to combine the circuits you'll have to connect a reference on one circuit with a reference on the other one. In 99 % of cases you'll choose the resp. grounds for this, because that's what ground is for: a reference against which all the rest is measured. If there's a 3 V level in a circuit, it will be referenced to ground, unless specified otherwise.

So by connecting the ground of a 5 V circuit to the ground of a 12 V circuit the 5 V becomes meaningful for that circuit as well: it will also be 5 V, or 7 V less than the 12 V.

A well designed circuit must have a reliable ground, which means that the 0 V at one point should be as close as possible to that 0 V at any other point of the ground net. Zero difference is not always possible if you're working with high currents, but the difference should be as low as possible.

Aren't these the same as transimpadance amplifiers?

Well, yes and no. Technically, any current to voltage converter can be called a transimpedance amplifier. However, when dealing with opamps this generally refers to a configuration where the current is injected directly into one of the opamp inputs and the feedback resistor does the voltage conversion. The answer you link to is a good example. The big problem with this approach is that the conditioning electronics is tightly constrained by the need to return all the current through the load into the amplifier. For multiple sensors this can be difficult.

The current monitor, as shown above, isolates the sense element from the amplifier. This has good and bad consequences. On the plus side, it's easier to measure multiple sensors, and good frequency response is easier to guarantee. On the minus side, you have to insert a separate monitor element into the current path, and the usable gain is typically a good deal less. Also, the transimpedance configuration potentioally injects noise directly into the opamp, which can cause unexpected and intermittent problems.

Which approach one chooses depends on which considerations are more important.