Well, I'll try.
When I first noticed this, when using both Nikon film cameras and a FF DSLR with the same lenses, I called Nikon Pro services. I said that I was seeing about a 1/3 difference in DOF between the digital and the film camera with the same lenses. The reply was - that's about right. If you'll notice, around the time digital sensors became useable, Nikon (and others) dropped the DOF scales on their lenses as they no longer applied when used between media/formats. I'll date this with the Nikon manufactured Kodak 14N, the first popular FF Nikon F mount body (built on an N80 cam).
I have a pal who designs camera sensors, big ones used in oil exploration. He told me that the difference is reasoned by the attack angle of photons interacting with silver halide rocks and photo sites, The silver rocks can accept a photon at any angle, a photo site requires that they hit at 90 deg. Some makers have experimented with pointing sites off angle to more closely emulate film. The loss in site real estate (resolution) was the cost. Now many of the newer lenses are designed to point light rays at 90 deg to the sensor helping with resolution. But the “better ilusion” of depth requires the more friendly acceptance angle of the silver rocks.
As for the difference between FF and APS-C, that’s a function of the lens (formula). A 200mm is a WA at 8x10 and a telephoto at 35mm. The formulas change for coverage but you can’t cheat physics when DOF is measured.
As for Depth of Focus (not Depth of Field) my designer pal said that focus is much more critical with a sensor than with film. He thought that it would be tough to sell digital cameras without AF. While Pros and many advanced amateurs can properly focus a camera, few high end digital camera owners would have sharp photos without the use of AF. Personally, I use AF a fair amount but turn it off when I see AF errors. I find that I can focus critically with a digital camera almost as easily as with a film camera.
Here’s a citation that may help:
http://www.rodenstock-photo.com/mediabase/original/e_Rodenstock_Digital_Lenses_3-26__8236.pdf
Just an observation:
Not very long ago, there were many on this forum that could explain this kind of technical bit much better than I have. I miss reading their posts.