The results are impressive, but what makes this 4D? Where’s the extra dimension and how is it relevant to 3D human beings?
You can move a virtual camera 3-dimensionally within the scene at any individual frame (x, y, z), and also move the scene through its animation to play the animation forwards and backwards (in other words, you move the camera through the 'time' axis).
So, like the scrubber in any video? Doesn’t feel like that warrants the 4D moniker. Which is not to say you’re not right, I think you are and that’s what they mean, but it that being the case it feels more buzzword than anything.
You are correct though, they both serve the same function.
However, I’ve yet to see a video player that lets you reposition the camera as if you were using photo mode in a video game. That’s (essentially) what this thing offers.
and synthesizing a (limited) model with 3 spatial dimensions, plus 1 time dimension.
3D over time is colloquially called "4D;" though we don't call video "3D" by analogy as the term binds strongly to its purely spatial use.
Colloquially, meaning “used in or characteristic of familiar and informal conversation” 4D films have a definition, and that ain’t it. 3D over time is colloquially still referred as 3D, as evidenced by decades of 3D blockbusters.
I've been interested in the state of the art in that domain myself, having thousands of 2D videos I've shot which I would love to see "spatialized" well, someday.
There's the 2D frame and the time dimension. Then there's the structural information conveyed by motion, parallax, scene composition, camera movement, etc.
That's why there's the 180 rule, amongst other things.
Algorithms can take a video and turn it into a 4D volume. As can our brains.