The Difference

The difference among all these three is quite simple. Moving oscillator is the most general approach, and moving mass and moving force are two extremes. In moving force we account for only the load being transferred to the bridge due to vehicle's weight and the inertia of the vehicle is ignored (i.e. mass effect of vehicle is ignored). Moving mass is another extreme where the vehicle is assumed to be rigid, and the weight and well  as inertia forces are transferred to the bridge. So in other words, moving mass and moving force are specialized form of moving oscillator case. Which extreme you want to use is dependent on the mass and stiffness of the subsystem (i.e. vehicle) w.r.t. the primary system (bridge).

------

The world started with 0, is progressing with 0, but doesn't want 0.