Initially I used 3d objects made in blender, a simple flat disc, and a box/rectangle, I put the rectangle below the flat disc, gave them both colisionshapes on rigidbody3d, gave the rectangle an animationplayer, it moved back and forth. I hit play, the flat disc fell and landed on the rectangle, but while the rectangle was still moving the flat disc just stayed there?

So, I thought, maybe due to blender models.. So, I used primitives in the engine, a capsule above a box, again, gave them the collsion3d and all that good stuff, I actually gave the box an animatablebody3d. Hit play, and the capsule fell on top of the moving box, but just stopped.

In both instances, I was expecting the falling objects to land on the moving objects and then move along with them?

What am I not understanding? To do what I'm trying to achieve (move the falling object with the object it landed on) do I need to use code?

Try adding friction by adding physics materials. Friction might be good enough, but if not, there are still more options.

You can code _integrate_forces and manually add the movement behavior you want.

You can add the Jolt Physics plugin and use a conveyor.