On a thermostat, are "R" and "Rh" terminals the same thing?
R in general
R, Rh, and Rc are all the same, but not.  In general terms, the R terminal is where you connect the signal voltage source. In low voltage controlled systems, there will be a step down transformer that provides the power to the control circuitry.  One of the legs from the secondary of the transformer will be connected to the R terminal, which applies a voltage to the terminal.
When the thermostat wants to be warmed up or cooled down, it closes the appropriate switch, completing a circuit.  This allows current to flow from &quot;into&quot; the R terminal and &quot;out of&quot; the appropriate signal terminal (W, Y, etc.) of the thermostat.
R, Rh, Rc
In some systems, both the heating and cooling systems use their own signal voltage. In these cases, the signal wire from the heating system will be connected to R or Rh, while the signal wire from the cooling system will be connected to Rc.
If only a single signal wire is used, the R terminal will be electrically connected (jumpered) to Rh and/or Rc.
This answer has some diagrams that show how a simple single signal system works. This answer provides another diagram of how a single signal thermostat works, though you can easily imagine how it could be modified to allow multiple signals.
A multiple signal system would look something like this...

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