Inverter makes 120 volt out of 12 volt
Converter makes 12 volt out of 120 volt
Many inverters have and optional "Bonding" feature (or none at all)
If the bonding feature is set to "not bonded" (Often it's a screw that fits in one of two holes) then you have an open neutral when the inverter is in operation.
If the neutral is not properly connected to the green wire/screws on the inverter.... It really messes things up.
Larger inverters often contain a transfer switch.. With shore power... All 3 leads "Pass through" so bonding is done at the service master (park in this case) as code requires.. But when operating on "Inverter" (Battery power) it's up to the bonding setting. NOTE not all inverters have this.
But you said when on inverter you only get 100 Volts... MSW inverters will often read low on a "Peak reading" volt meter.. Most low cost volt meters are Peak Reading... (I have some True RMS types the MSRP on them (not what I paid) is over 200 dollars.. (Got 'em at a "Fire Sale"for less than half).
For more detailed reply I'd need make and model of the Inverter and/or eyes on.