One of the reasons that, as is often said of trying to keep a Jag running in the US, "All the parts that fall off are of the finest British manufacture."
And there are lots of WWII stories about trying to fix Sherman tanks and Jeeps with Whitworth fasteners.
Actually, UNC is Unified National Coarse, pretty much the same as the old USA standard which was SAE (Society of Automotive Engineers). The difference is in the small radius at the bottom of the V. I can't remember what the change was for sure. I think the USA thread had a sharp V at the bottom of the thread, and the Unified National Thread (adopted by US, Canada, and I'm not sure who else) has a small radius. The old SAE threads will fit just fine with the newer Unified thread.
The world's most common thread? This must be the 1/4" x 20 t.p.i. Whitworth form found in the base of a camera that allows it to be fitted to a tripod or other mount. It's common to every camera maker and every model they produce - though some heavier professional types have, as a concession, fitted with a more robust 3/8" x 16 t.p.i.
It's 1/4" and 20 tpi no matter what you call it. The only difference is the core diameter. 0.186" for UNC and 0.1887" for Whitworth.
It's not about what you call it. It's designation of a codified standard. You can have a 1/4"-20 tpi box thread and that isn't going to fit a 1/4"-20 Nation Coarse which is sharp V (60 degree). Threadform is just as important as size and pitch. Even if the wrong pitch "fits" because it is sloppy enough means it will wear quicker and all need replacing.
The minor diameter difference is because Whitworth has a steeper thread, thus the root diameter is larger because the depth of the thread is shallower off of the major diameter of the screw.
Yes, One has a 55 degree cut angle and the other is 60 degrees. I forget which way round it is. As you say, if you put the screw of one into the thread of another there will not be a flat to flat surface bearing the force. It will work but will wear with continued use.
The original difference of opinion here was with which thread was used. I claimed Whitworth but others (usually Americans) thought it was UNC. The fact that many cameras were made with 1/4" x 20 tpi threads before UNC was unified makes me think that it was originally Whitworth.
The 1952 ASA standard tripod screw specification is 1/4 - 20 TPI UNC-1A thread (and 3/8 - 16 UNC-1A for larger cameras) on American cameras. Perhaps in England the Whitworth form was used. Several variations of T-nuts and threaded inserts in these sizes are readily available over the counter in Ace Hardware Stores in America. David Goldfarb gives good advice above on mounting a T-nut so the tripod pulls it against the wood of the camera rather than relying on little screws to hold the T-nut as seen in some imported pinhole cameras.
Ah, I suppose camera/head vintage now becomes important. I was basing some of mine off of the measurements I took from my cameras and fittings. It would make sense that a really old camera would have a different threadform.
My original understanding was that the discussion was counting diameter and pitch as the important pieces of a screw, not the form; rather than the idea that diameter/pitch has been relatively standard but threadform has changed.