Most of the PLUG IN type inverters,, if not all, are MSW devices.. Now MSW depending on who you talk to means Modified Sine Wave, or Modified Square wave.
If you look at the waveform on a 'Scope it looks like a Stile (The steps a farmer uses to get over a fence.. also a name for a pile of dung).
On a sine wave the peak voltage is 1.414 times the RMS. so if you have a "Peak reading" voltmter.. they multiply by 1/1.414 (I think that's .707 but don't quote me) to give you an RMS reading of 120 volts.
BUT the Peak reading on the MSW is way lower so the peak reading voltmter gives you a lower reading since it does not know better.
I have both Peak and TRUE RMS meters (RMS is the area "under the curve" that is the area between the sine wave and the base line (0 volts) and that will be the same with your inverter as with mine (True Sine Wave)..