First off, an inverter does not charge 12VDC. An inverter provides 120VAC from a 12V source.
You may have an inverter/charger but that is only common on upper end units unless after market installation.
What you probably have in a converter/charger. The converter changes 120VAC to 12VDC while the charger uses 120VAC to charge the battery bank. What you are seeing on the guage is what the charger is using to charge your battery bank.
If you do have an inverter/charger that same guage may show your power consumption when on the inverter.