If you look closely at the gearboxes you use for examples, the ones you have listed as 3:1 have three small bearings on the side of the box. Now go to the ones you list as 4:1 and you'll see it has 4 bearings visible. There's an extra, small reduction gear right at the pinion, giving these an extra reduction gearshaft, for a total of four shafts in between the pinion and the gear on the axle. The first sets you show (3:1) don't have that extra shaft and there's only three shafts in between the pinion and the gear on the axle shaft. That's why the 4 shaft boxes are only available in high/low configuration, because on a mid or low you can't get that fourth shaft in there. This is why I refer to them as 3 shaft and four shaft gearboxes. The main problem was that the old hippie brain got too confused and needed a quick way to identify the difference, so I thought, "why not just count the gearshafts that have reduction gears on them". The 4 shaft have an extra reduction gear.

The suppliers starting this 3:1 and 4:1 stuff just made it confusing for us all. The true final drive ratio is easy to explain, how many times does your pinion gear have to turn to turn the axle one rev? If your pinion turns 100 revolutions to make the axle turn one revolution you have a 100:1 final drive gear ratio (or vice versa, I already said I always get that mixed up so it might be 1:100). Easy to explain, much more difficult to calculate. I'm not going to turn that tiny little pinion by hand to find out how many times I have to turn it to make my sprocket go around one time. I bet it's a lot! I guess one way would be by RPM, if you had something that can detect pinion RPM and axle shaft RPM, like they use for airplane props, but I don't know of any such device.

I agree with Dan that you should not have deleted your post. The tooth count info is very helpful when changing the pinion gears. Now I wish I had made a copy of that. There's no such thing as too much information.