As I understand it, 1/76 and 1/87 grew out of respective train scales for the US and the UK. Sometimes they are referred to as HO or OO scale (HO being "half O"). The train track widths are the same, but for OO, the Brits scaled things a little differently and it came to 1/76 (I can't recall if UK and Europe railways are narrower than typical US based railways). Since I believe US railways are a little wider, scale the rest of the locomotive to fit a same dimension piece of track and you get a smaller number (1/87).
Of course, how it applies to military stuff, Roco Minitanks in Austria for many years was making a set of pre-built armor from WW2 up to modern day and they did everything from towed artillery pieces and jeeps on up to main battle tanks (they even did some airplanes and helicopters). Airfix in the UK seemed to be the originator of 1/76 as they did many of their tank models and figure sets in that size. Although you look at them, they don't really look all that different from 1/72. So ultimately, things got re-labeled to the 1/72 size (such as in the US when MPC was importing some of the Airfix armor and re-labeling it to conform with the more popular 1/72 aircraft scale). Stick 1/72 and 1/76 armor together and you can't really tell any difference (kind of like sticking 1/24 and 1/25 scale car models together). Even Airfix themselves started mixing stuff together in thier diorama models as you might have an RAF base diorama with a tower, two refuelling trucks, figures and a Spitfire (and all are labeled 1/72). But, I have seen exactly the same trucks labeled as 1/76 when by themselves (same with the tower).