Actually, it's the converter/charger that produces 12VDC to the battery when connected to shore power. To check the battery charge, you'd need to disconnect from shore power and use a VOM at the battery terminals.
Voltage when connected to shore power will be what the converter/charger is putting out which will depend on the charge state of the battery and the time you've been plugged into shore power. The WFCO converter (usually the brand in Keystone products) produces 3 charge voltages which are controlled by time and the battery charge state. They are:
Boost (Bulk Mode) 14.4 VDC
Nominal (Absorption Mode) 13.6 VDC (includes charging and load)
Trickle (Float Mode) 13.2 VDC (after 48 hrs.)
So, depending on your battery condition, you could be reading any of the above three voltages, or possibly less if you have a heavy 12 volt load on the RV. This could occur with heavy incandescent light use, operating the slide, water pump, landing gear/stabilizer jacks, etc...
Voltage when the battery is isolated from shore power will depend on the charge. This is a close approximation of charge status, but it is NOT exact:
100% 12.7 VDC
75% 12.4 VDC
50% 12.2 VDC
25% 12.0 VDC
Discharged 11.9 OR LESS
On your "4 LED Monitor Panel" you'll see these voltages represented by the number of LED's that are shining.
There is a difference in a "converter/charger" and an "inverter". A converter charger changes 120VAC to 12VDC (and charges the battery). An "inverter" changes 12 VDC to 120 VAC and uses battery power to provide AC when the shore power is not available. Most travel trailers do not have inverters as a factory option. You most likely do not have an "inverter" in your trailer.
Actually, the best way to determine "charge status" of the battery is to use a hydrometer and check specific gravity. Most of us don't carry a hydrometer with us, so voltage is a "next best" substitute.
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS