let's say the following:

TRMS meters generally have AC and AC+DC modes, but usually your interested in the AC portion.
The TRMS voltage of a waveform will have the same heating value of a DC voltage set to the TRMS value.

AC meters have a frequency response. They also might be limited by the crest factor of the waveform.
There were thermal AC TRMS meters at one time.

Non TRMS meters are what you might call. Average reading, TRMS responding.
What does that mean? Take line voltage of 120 V 60 Hz sine wave. It flips the voltages below zero (i.e. precision full-wave rectify and it averages. Throws it into a capacitance filter. The result is the average value.
The meter then multiplies that average value by a constant so it reads the RMS value of the hypothetical sine wave.

The meter basically assumes it's being fed a sine wave, averages whatever it gets and multiplies by some k.
if you feed it a 60 Hz sine wave, you will get out the RMS value of the sine wave.

We talk about average, but the average of a typical sine wave is zero. it's really the average of the absolute value.of the waveform.