While watching All the President's Men, my friend pointed out that cinematographer Gordon Willis uses deep focus in many shots to keep both the background and foreground elements in focus. This is just a quibble, but the movie actually makes use of a tool called split diopters to achieve an effect that's similar to deep focus.
In this scene, Bob Woodward, played by Robert Redford, attempts to listen to crucial information from an informant while his oblivious coworkers host a party that overshadows his conversation. One approach may have been to "rack" (or switch) focus between Woodward and his coworkers. Here, Willis decides to draw our attention to both Woodward and the loud coworkers equally, so we realize more fully what is at stake if Woodward can't hear his informant over the hubbub.
In Citizen Kane, cinematographer Gregg Toland used a technique called "deep focus" to achieve a similar result, perhaps most notably in the scene where a young Charles Foster Kane plays in the background while his parents sign his life away.
So both techniques end up drawing viewers' attention to all of the planes in the mis-en-scène. The techniques, however, are quite different.
Roger Ebert defines deep focus as:
"… [A] strategy of lighting, composition, and lens choice that allows everything in the frame, from the front to the back, to be in focus at the same time. With the lighting and lenses available in 1941, this was just becoming possible."
Have you ever wondered why it's easier to see or read at night when the lights are turned on? That's because the extra light makes our pupils smaller, effectively making the aperture smaller, thus increasing our eyes' depth-of-field. Deep focus achieves a similar effect with camera lenses, except that a huge amount of light is required to achieve that same, increased depth-of-field. And considering how insensitive, or "slow," older film stock was, Tolland would have had to use lots of light.
A split-focus diopter, on the other hand, is an optical adjustment that became popular in the '70s. Wikipedia describes how it works:
A split diopter is half convex glass that attaches in front of the camera's main lens to make half the lens nearsighted. The lens can focus on a plane in the background and the diopter on a foreground. A split diopter does not create real deep focus, only the illusion of this. What distinguishes it from traditional deep focus is that there is not continuous depth of field from foreground to background; the space between the two sharp objects is out of focus. Because split focus diopters only cover half the lens, shots in which they are used are characterized by a blurred line between the two planes in focus.
You can see that line of demarcation in the above screengrab from All the President's Men.
So in short, one method requires major lighting setups to achieve a greater depth of field, while the other method uses an optical solution to create a similar effect. A small, but important, difference.