Brenda & Dave and Darren
I think you may be starting down a tricky path here trying to compare D.C. and A.C. electrical systems in your trailers.
These systems are seperate and dis-similar aside from the fact that they both control electrical items.
In a D.C. system there is a 12volt positive and a negative or ground cable.
All 12volt circuits run on these two wires.
For reasons I will never understand there are two different conventions used to mark the wires and they are exactly opposite.
In some the red is 12v positive and in some the black is 12volt positive?
If you buy a cheap multi-meter you can easily determine which you have for any given 12vdc circuit. They are also very handy for many other uses and under $20.00 at a home center....get one.
In a trailer you can ground a 12vdc outlet or fixture to the trailer frame and then just run a single conductor wire to the Positive load. Most small trailers come wired like this, but I always just run two conductors with a dedicated ground to each fixture. Most wire is two conductor anyway and it is a lot more reliable to run the ground on a wire rather than through the trailer frame especially for us as the trailer body is non-conductive fiberglass which can make frame grounds unreliable.
It is then a simple matter of running your load wires to the battery directly or if you want more control through a switch or switch panel so you can control them from a central point.
Likewise you will need to charge the battery and you can connect the charger directly to the battery too. It may be Solar or it may be a house powered charger but either way it will output 12volts DC to charge the battery.
Some of these will also supply enough 12volt DC power to run the trailer while your battery is charging. some will not.
This is a very simplified overview for sure but 12volt DC systems are fairly straightforward really.
The 120volt AC system is like a residential house system and the three wires are not directly comparable to that of the 12volt systems and should not be interconnected directly!
There is a device many trailers have and that you can add called a "Converter" that will supply both 12volt DC power from 120volt AC power and charge your battery and supply 120volt AC power when plugged in.
They can act as a central point for all of the wiring and simplify things a lot.
I hope this clears up some of it and there is a wealth of other info out there on this site and many others.
I recommend a West Marine catalog as they include basic info on all of these systems and feature equipment to make it all work in a single free catalog.
Remember if you don't know,please find out. This stuff can be bad if done wrong.
And Have Fun.