One of my pet peeves: "rms power".
If you measure the rms voltage V across a known resistance R, then the mean power is V2/R.
This is true for any waveform, including DC and an AC sine wave.
As an exercise for the reader, you can compute the "rms power" for a sine wave, which is 22.5% larger than the mean power, but is a useless parameter.
With a device that measures the instantaneous value of the voltage V(t) and the current I(t), then their product W(t) = V(t) x I(t) is the "instantaneous power", and the time average of that power as a function of time over a long time is the mean power, corresponding to the meaning above for a voltage and resistor.