We need to make sure our definitions for control and reading of heat isn't crossed either. Just as a clarification:

Thermostat = device to directly control the energy output of a heat source. A thermostat needs to have a probe attached to detect the temperature of the heating element it controls.

Thermometer = device to read the heat outputted by a heat source. Thermometers can have a probe but not always. Probes for thermometers are like probes for thermostats, they both register the heat generated.

Dimmer = rheostat = device to limit the electrical current to an attached device. Great for ceramic heat emitters (CHE) as it can limit the current thus limiting the heat on the surface of the CHE without needing a probe. You do need some way to measure the heat inside the tank in order to adjust up or down the dimmer switch.

For an under tank heater (UTH), the thermostat probe goes outside the tank in direct contact with the UTH, for thermometer probes, they go inside the tank and for hot side reading, the probe goes under the substrate at the warmest spot inside the tank.

Making sure everyone is speaking the same language