As for the three and four shaft names, I just thought it was a quick and much more accurate way to identify gearboxes at a glance. Perhaps this video will clear things up. All I'm really after is for us all to be on the same page. What term we finally decide on doesn't matter. The three and four shaft names aren't supposed to have anything to do with gear ratios, it's just a quick way to identify which box it is.

https://www.youtube.com/watch?v=rKz1rTDO2qY