As to your original question - Converters convert 120V AC to 12V DC to power your 12v lights
& appliances & charge your batteries.
Inverters convert your battery's 12V DC to 120V AC and can be used to produce 120V AC when you don't have hookups.
There are combination devices that are both inverters & converters, but they are expensive - in the $2K-$3K range.
The problem, as Glenn mentioned, is since the wattage is the same at 12V as it is at 120V, and wattage = Volts X Amps, the inverter draws a minimum of 10X the amperage from your batteries that the device uses. They work fine of low power loads, or, properly sized, OK for short duration medium to high wattage loads, but an AC would kill your batteries in a couple of minutes.
While a large enough battery
pack might be able to run your AC, it probably would weight
a significant part of your trailers weight
. I know of one individual that powers his RV's AC with an inverter. It is a 3000 Watt inverter/charger & he has a battery
system consisting of 8 6V, 232 amp/hr batteries (520 lbs of batteries). Even then, he only runs it to cool down his RV, then shuts it off.
I use a 1000 watt inverter to make coffee. I draw 60 amps @ 12V for 6 minutes from a pair of 6V, 232 amp/hr batteries to make a pot. To do that I had to install large sized wiring between the batteries & inverter, use a pair of 6V batteries, and expect to take at least an hour for my solar
system to put back what the pot of coffee took out. For me it is worth it for a great cup of morning coffee, but without the solar
system it would severely limit my ability to dry camp.