A buzz is a different problem. That comes from the AC power line. Or more accurately, the twice-per-cycle current spikes that happen when a DC device is cheaply powered from AC, because that's how a rectifier-capacitor works. It draws nothing until the incoming AC voltage is higher than the capacitor voltage, and then it draws all of its current at that moment to recharge the capacitor. Then it draws nothing again for the next half-cycle of AC.
This is true for both the old classic "linear" power supplies (mains AC -> transformer -> rectifier -> capacitor -> DC load) and the cheaper switching power supplies (mains AC -> rectifier -> capacitor -> high-voltage DC -> isolated DC-DC converter -> load).
A more expensive power-factor-corrected (PFC) switching power supply removes the high-voltage capacitor and has two stages of DC-DC conversion:
mains AC -> rectifier -> DC-DC boost -> super-high-voltage DC, still variable, and capacitor -> isolated DC-DC buck -> load
As you can see, the first DC-DC converter boosts to an even higher-voltage DC than what the mains AC can provide, with some extra logic to try to make its input current follow the input voltage, and then the second reduces that (still variable) super-high-voltage DC to what the load actually wants.
Another source of a power-line buzz is triac-dimmed lighting. These are cheap, and appear everywhere from residential wall-mounted dimmer switches to multi-kW-per-channel theatrical rigs. The triac itself is just a switch, with surrounding circuitry to keep it off for the first part of each AC half-cycle and then turn on to finish the half cycle. The ratio of on to off (called the duty cycle) determines the brightness of an incandescent bulb, or the speed of a (small!) motor. (they're really not designed for motors, but sometimes they work anyway) The shock of current starting when the switch turns on, which happens twice per AC cycle, can also cause a buzz in other gear. Sometimes the bulb or motor itself will buzz, because some part of it is acting like a (crude) speaker, with the electrical power as its signal.
In either case - rectified AC -> DC, or triac dimming - the primary pickup in other gear is induced through an air gap. Inverse-square law, times the length of cable at each distance. So the way to reduce it is to keep them apart, and if they must cross, do it at a right angle.
Shielding helps too, so that both ends of the problem "connect" to the shield instead of directly to each other, and the shield itself is connected to ground so that it doesn't wiggle electrically. (if the shield is not grounded, then it does wiggle electrically, and so the system works as if the shield were not there at all)
And twisting the wires helps a lot for balanced signals, because it puts them in effectively the same place on average, and so they pick up that noise equally. Equal pickup in a balanced signal, drops out at the receiving end, because it only cares about the *difference* between the two wires.
XLR runs, from stage to sound board in a pro rig, are shielded twisted pairs that carry balanced signals, so they use *all* of the tricks above to reduce or eliminate noise. That's how a raw, unamplified mic can go that far through an environment that also has high-power triac-dimmed lights and who knows what else, and still have a clean signal after the board's preamp.
That's probably WAY more than you wanted to know. :-) I just wanted to provide enough detail to show how different sources of noise have different sounds, so that you can rule out a lot of problems just by how they sound. More skilled ears can also diagnose radio and digital problems based on how the decoded audio sounds.
TL;DR:
- A buzz is almost always related to an AC power line.
- A hiss is almost always from the gear itself.
Completely different problems with completely different solutions.