You basically have it down as to 120V vs. 120/240V for residential wiring.
A 240V circuit (in North American single-phase wiring) is made from two 120V circuits that are 180 degrees out of phase with each other. There is a 120V potential between either of them and neutral, and 240V between the two hots.
A 240V breaker, then, basically consists of two individual 120V breakers physically tied together so they trip at the same time when either one overloads. There are circumstances where such breakers are used for two 120V circuits rather than one 240V circuit (usually where the two circuits are sharing a neutral), and many common 240V devices are actually 120/240V devices, rather than pure 240V devices, and so may not load the two legs equally.
A 120/240V panel does have two hot busses, and you'd only use one. The main breaker would presumably still be a dual breaker, but you'd only connect one side of it and leave the other one dead. (You don't want to connect the hot to both sides of the main breaker as that would permit twice the current in the worst case...and, depending on the specification of the panel, could also overload the neutral bus that normally only needs to carry the difference in current between the two legs, rather than the sum.) On some panels, those with power take-off lugs connected to the main hot buses, you could presumably also bridge them between the lugs, still using only use half the main breaker, to get more slots available for load circuits. I don't actually know if this would be up to code, but I don't see how it would be inherently dangerous.
You need a master breaker or fuse for a couple of reasons: first, to prevent an overload in the system as a whole. In your trailer, for instance, without the master fuse you could in theory have 40A flowing through the system designed for 30A with just the branch circuit fuses. Second, and just as important, it also serves as a master disconnect for the system so you can remove power in case of an emergency or for doing repairs etc. I guess a third reason is simply that the electric code (generally) requires it, for better or worse, with a few exceptions for quite small systems.