You are correct. Residential refrigerators for RV's will now come in 2 flavors: DC or AC.
DC (12 volt) residential refrigerators will run directly off the battery 12 volt system always. Of course, when hooked up to shore power, your converter is charging your battery, and all the 12 volt devices throughout the entire camper are drawing power from a combination of the battery and the converter.
AC (120 volt) residential refrigerators run only on AC. But! a device can be installed in the camper that will convert the battery (DC 12 volt) to AC 120 AC volt. This is called an inverter.... notice the difference:
"Converter" input is AC, output is DC
"Inverter" input is DC, output is AC.
A residential refrigerator in an RV will require one additional piece of equipment .... a transfer switch.
The transfer switch will automatically switch power going to the refrigerator to ensure it always received 120 volt AC electricity. The transfer switch has 2 "inputs" .... both AC from shore power AND DC from the battery.
The transfer switch detects when the camper is plugged into shore power. When it is, the transfer switch switches the "input" from AC shore power. When the camper is disconnected from shore power, the transfer switch will detect the loss of AC electricity and immediately switch it's input from the "inverter" ... via the battery.
This keeps the refrigerator running continuously without interruption when plugged into shore power and when not.
Now, the challenge is to keep the battery charged (and that's a topic for someone else to piggy-back on).
A residential refrigerator inside your camper will function exactly like a refrigerator inside your house. If your house looses power, you have "X" number of hours before things begin to get too warm inside, and "X" number of hours before the ice cream in the freezer section begins to melt. Every refrigerator is different here, regarding it's longevity to remain cold without power, and it also depends upon the ambient temperature around the refrigerator too. If no power, Ice Cream will begin to melt a lot sooner if the ambient temperature is 100 degrees, opposed to it being only 50 degrees.