1. The 12 volt and the 120 volt (used to be 110 many years ago, now is 120) differ not only in the actual voltage but in the type of current. The 12 volt we are using is DC, direct current. The 120 volt we are talking about is AC, alternating current. DC is what batteries supply; AC comes from the power grid, generators and inverters. Inverters are powered by the battery or batteries. AC has a hot wire (usually black) and a neutral wire (white) and a ground wire (green or bare). DC has a positive wire (often red) and a negative wire (often black).
2. Batteries that we would use in a trailer come in 6 VDC and 12 VDC versions. Add two 6 VDC in series (connect the positive of one to the negative of the other = 12 VDC). Add enough cells or batteries in series and you could have 120 VDC, but we don't need that in a trailer.
3. AC and DC do not mix and are not interchangeable. But 120 VAC can be used with a battery charger to charge 12 volt batteries and 12 VDC can be used with an inverter to supply 120 VAC. There are certain limitations we won't go into now.
4. If you don't have a basic understanding of electricity possibly the best way to handle it is to install something like a
PD 4045. It gives you a battery charger and both a DC and an AC power distribution system, all in one unit. You still need to wire up the lights, plugs, etc but it is a solid unit to base all the electrical needs upon.
5. As for charging while driving down the road there is at least one topic here on that but I am out the door right now. Maybe someone else can pick up my slack on that. It is done via a plug and socket connection between the TV and the trailer. Again certain criteria and limitations.