I had a look at an AIMS inverter/charger manual and you may be thinking about the automatic neutral to ground switching feature. When plugged in, the shore power main panel AC ground and the inverter AC ground are connected as they normally would be. At the main panel (and only at the main panel) the neutral and ground are connected together. This makes the breakers work properly. Don't ask me why.
When on inverter power there is no "main panel" so the relay connects the AC ground and neutral at the inverter so the breakers will work as they should. This, in effect makes the inverter the main power panel.
It's best to think of all this as magic.
At any rate, there is a ground lug on the inverter case that should be cabled to a good body ground.