I am trying to find a theory similar to Roland Barthes' for the photography, where he describes a detail in a photo as "punctum", that creates a direct relationship between the object and the person within it. Is there a such a thing for the movies?
I think you could directly apply the term punctum to a motion picture medium as well as the still medium for which it was originally written.
Punctum is defined as "that which pierces the viewer", so it's basically the details that make the photo (or film) connect with the viewer and add authenticity to the scene. In still photos, this would arguably be much harder, except in the cases of cameo shots.
War shots, post catastrophe, and other "one time" situational shots basically create their own punctum, because they portay a moment of triumph/suffering that essentially can't be recaptured. Staged shots become much more difficult in a still medium, because you have to carefully arrange what you think will connect.
With a motion picture, you have a much broader spectrum of tools to choose from to immerse the viewer in the experience and evoke that emotional reaction/connection.
But for your basic answer, I am not aware of a separate theory for motion versus still photography that echoes Barthes' work.