I’m not a model railroader, but I can remember discussing this stuff I the hobby shop wher I used to work (longer ago than I like to think about). The conventional wisdom was that HO stands for “half O.” But that’s only approximately true. O scale is I/48; HO is 1/87.
Another theory is that some of the problem originated with the British. According to the theory, the British settled on a small model railroad scale of 1/76, which they call OO, and the Americans wanted to use the same track. Real European track is narrower than American track; 1/76-scale British track worked out to be 1/87-scale American track.
That scale of 1/76 got picked up by Airfix for its armor and soft plastic figure sets. (Anybody else remember those? Fifty cents for 48 figures at my local hobby shop!)
I think 1/72 scale got started by another British company, Frog. In the late thirties Frog introduced a series of 1/72 kits called “frog Penguins.” (FROG stood for “Flies Right Off the Ground - which other Frog models did, courtesy of rubber bands. Penguins don’t fly. Get it?) A few years later, the USAAF adopted 1/72 as the scale for its “recognition models.” I assume the attraction was that in 1/72 scale 1”=1’, so a human figure would be an inch tall. I hadn’t heard about “grille scale,” but it fits.
There’s a scene in the great movie "The King’s Speech in which the speech therapist rewards the future George VI by letting him glue a piece onto what looks like a Frog Penguin.
It’s interesting that the boxes of Airfix military vehicles sometimes say 1/76 and sometimes 1/72 - though the kits are identical.
A guy who used to wort for Monogram told me that the company was proud to be a leader in 1/32 scale for military vehicles. On 1/32, you can measure stuff with a ruler marked in 32nds without doing any complicated conversions. Every 1/32" on the model equals an inch on the prototype. I imagine the popularity of 1/35 in Japanese kits had to do with the metric system .Nowadays Tamya makes 1/35 vehicles and 1/32 aircraft. Ouch.
Most of this is based on my recollections of stuff I think I remember reading. I’m anxious to be corrected.
I’m on a long-term crusade to ban the use of “quarter scale.” When modelers say that, they almost invariably mean 1/48 scale, or 1/4"=1’. Given the current trends in the kit industry, one of these days some company is going to release a genuine 1/4 scale (i.e., 3"=1’) P-51, and everybody will be thoroughly confused. I think there are enough confusing things in the world. End of sermon.