This is a relatively complicated issue.
Voltage is a driving force, similar to the more usefully named "electromotive force". A higher voltage is analogous to more pressure from a pump, or more torque from an engine. Current is the rate of flow of electrons. More current is analogous to water flowing faster down a pipe, or the wheels on a car spinning faster. Generally voltage is controlled by the bios, the current that flows is whatever the resistance of the circuit leads to. More voltage normally means more current.
The voltage you're talking about is obtained from the 12V rail using the power control circuitry on the motherboard. The bits which get hot are mosfets, and generally have heatsinks attached to them. So 12V is maintained across this circuit by the psu, and whatever voltage the bios has requested is applied across the processor. A rule of thumb for your processor is that over 1.4V is a very bad idea, but the lower the better.
Now, for any power source (whether its the psu or the mosfets), the voltage output decreases with load. So, the more current your processor draws, the lower the voltage across it will be. This current is correlated with processor load, so running prime will make it use more power, so draw more current, and lower the voltage it is being supplied.
This means that the voltage set in the bios is what will be across your processor during no load, i.e. processor turned off or removed from the board. While idling in windows, the current through the processor is fairly small, so the voltage drop caused by this current is fairly small. This is vdrop, and the difference between bios voltage and cpu-z when idle. When under load, the current drawn increases and so the voltage applied decreases, leading to a cpu-z load voltage which is lower than the previous values. This is termed vdroop. Note that they arise from the same cause.
High voltages damage chips, think of water flowing down a pipe so hard that it starts to burst the seals at the joints. However high current also damages chips, if you made the pipe out of something that's slightly soluble in water you'd expect pumping water down it faster to erode the walls faster. So, both are bad. However it's high voltage with high current that is particularly dangerous, as then you have a high number of electrons going through the structure with considerable force. Temperature comes into this, in that when the silicon is hotter it is more easily damaged by collision from these electrons.
This leads to the conclusion that load voltages are most important. When idle, the currents are much less, so it doesn't matter as much that the few electrons in motion are moving violently. When under load, each electron has less energy associated with it, but an awful lot more are in motion. Also, under load, it gets hotter, so making it more vulnerable to damage.
The upshot of all this is that load voltages matter more than idle as they are more destructive, and that keeping the silicon colder gives you more headroom to increase the voltages. So, the answer to your question is that most of us work to load, cpu-z voltages.
A couple of notes on the above. I'm ignoring calibration errors, if worried that the bios' idea of 1.3V differs from realities just get a multimeter. Cpu-z normally compares well to multimeter readings so is generally trusted. The above discussion is assuming intels power delevery spec is followed, a lot of boards introduce load line calibration / disable vdroop as that's what enthusiasts wanted. This can be considered as dynamically increasing the voltage output by the mosfets with load to counter the voltage drop due to current. Main arguments against this are that it only decreases idle voltage, which is less significant than load, and that it works the board a lot harder so motherboards should fail sooner. Arguments in favour are that people can set a lower voltage in the bios which makes them feel more secure, and that high idle voltages are still dangerous even if they're less so than high load voltages.
