This topic has confused me for a long time. ...
That's because it's confusing. As is almost everything having to do with shielding, grounding, hum, noise, and RF interference. I'll do my best but I'm sure I'll be wrong in some way:
The wires between two audio devices can pick up noise, in the sense of unwanted electrical current or voltage. It can come from the electric and/or magnetic environment, or from the devices themselves.
Much of the available literature deals with currents flowing in the ground connection between the devices. The common analyses talk about magnetic fields, which are caused by such things as electrical motors and transformers near the audio system. If the ground connections make a loop, such as power line ground to device 1 to device 2 back to power ground, current will be induced into that loop and will flow in the interconnect ground wire. These days it is more common for such currents to come from the devices themselves, usually capacitive coupling inside the power transformer, from the power line to the signal ground inside the device. A third cause is different grounds; typically the video cable ground is not the same point as the power line ground. In all these cases, the current flow creates a voltage difference along the ground line of the interconnect, in proportion to its resistance which is almost but not quite zero. That voltage adds to the signal. There are other solutions, but the simplest is to minimize that resistance, in which case you would connect the shield at both ends (and use heavy-duty RCA jacks and plugs).
The other way noises are introduced is electrical fields which are coupled into the wires. They typically come from radio transmitters and unshielded electrical devices - now we're talking cell phones, radio and TV stations, light dimmers, drills, RC models, etc. There are many more of these devices than there were 100 years ago when interference was first studied (for telephone applications), which is probably why these issues are less widely documented. These electrical fields are picked up by wires like an antenna. They can be drained to ground at either end; the shield intercepts these noises and prevents them from reaching the signal ground wire inside the shield. This is slightly better than having the shield itself be the ground, as in a coaxial interconnect. The current of those noises going to ground still drops a tiny voltage as it finds its way to the earth, and usually the output of a source is less sensitive to those tiny voltages than is the input of the next device, because the source impedance is much lower. So usually it is slightly better to ground that end of the shield instead of the other. But it's not universally true for all devices, all cables, or all situations.
