And, Ohm could have added "1 mV is a LOT, in an amplifier", if there were amplifiers!
I always make an attempt to be pedantic about naming which ground I am discussing in any given context, and, hopefully, making those names descriptive of the function of the ground at issue. It is the only way I can think of to keep confusion at bay.
The addition of the third-wire Safety Ground certainly makes the issues more complex, but I can't imagine how we managed to survive as long as we did without it. A guitar-player buddy of mine from back in the day of no safety grounds received a very instructive lesson one evening on stage: He was playing his electric guitar plugged into his tube guitar amp, a mid-sixties Fender which of course had no third prong on the AC plug. It relied on a switch to assign one side of the incoming AC line to chassis through a capacitor. Thousands of amps were made this way. The idea was to set the switch for the lesser hum, which usually meant that AC neutral was connected to the chassis through the cap.
Now, the chassis was the all-purpose "ground", of course. EVERYTHING "grounded" to it! Need a "ground"? Just solder to the chassis. So, ultimately, his guitar was "grounded" to the amp through the shield on the unbalanced guitar cord, which meant that the guitar bridge, and therefor the strings, were also "grounded" to the guitar amp. This also meant that the guitar was assigned to one side of the AC line, by the "grounding" switch on the amp.
All of which posed no particular problem as long as the guitar and amp and player were a little island unto themselves standing on stage.
Then, he stepped up to the mic to sing. He remembered a blue flash and running into the kick drum, but not a lot else. Seems the "grounding" switch on the PA amplifier was set to the opposite position of the one on his guitar amp. Which also would have been fine, if he just hadn't got his lips so close to that "grounded" microphone!
