I know the type of heater where there are two electrodes placed in the water and the electrolytes in the water complete the circuit to produce heat. Hot steam vaporizers use this principle. The electrodes were in a Bakelite tube at the top of which was the vent for the steam. I think I read in the directions for one we had not to add salt to the water because it could make it boil so violently it would boil over. That said, I don't understand how this type of heater could be used in a stock tank because the cattle would be knocked off their feet when they touched the water. Maybe it was a sealed rod type heater but your mom did not want you to risk being shocked by stray current leakage or something. Maybe she was just being a mom keeping her child safe. It would be neat to dip the base of a light bulb in the water being heated and watch how brightly it would light. When I was going to school we were always warned in health and science not to have a radio in the bathroom that was near enough to the tub or sink to be touched or that could fall into the tub. There were also "true crime" stories where people were murdered that way.
I remember reading in an electrical manufacturing magazine about one salesman's encounter with a woman when he was trying to sell electric water heaters sometime after WWII. She became very agitated and negative over the topic. When he asked why she related the experience of heating wash water in a tub in the basement. She would fill the tub, she said, then place these two paddles in it that plugged into a special box. Then she would leave the basement, lock the door and go to the fuse box elsewhere and turn on the current. Once the water was hot, she turned off the current, unlocked the door and went down to the tub of hot water, removed the paddles and started the laundry. Once he explained the difference between the way she heated water and a storage hot water heater she "warmed up" to the idea, but the danger of what she had to use before that was graphically remembered. I don't doubt that what she had to use was a 220 volt apparatus and certainly lethal.