Yes that is exactly correct.
We use the generic terms three series and four series simply because more often than not people are jumping into the fours ingearing.
Even though the changeover actually happens while still in the threes
I think we use the generic term three series and four series because the Australians down at ARB wanted to take revenge on the US. The carrier split on the Dana 44 was between 3.73-3.92 So it causes mass confusion when the same terminology is applied to the Dana 60, which has a carrier split at 4.10-4.27 and the Dana 30 which has a carrier split at 3.54-3.73.
I never remember hearing the term 3 series and 4 series before the late 1980's. (The Dana 44 2.88 ratio and the 5.38 ratio of course are neither 3's nor 4's.) Before that, the Dana Spicer power-lok cases were labeled "man" and "auto." It's only when the aftermarket started making full case lockers that the naming became interesting. Even though Dyneer / Tractech had full case Detroit No-Spin carriers, I think it was ARB with the RD-06 that started that 3-4 series nonsense. I do remember some literature that referenced "low vs high" ratio carriers, which led to the endless verbiage of "low ratio, high numerically" descriptions.
The launch of the 2003 TJ Rubicon Dana 44 with the Tru-Lock broke everything. For whatever reason, Dana paired a 3 series carrier with 41/10 = 4.10 gearset in a standard rotation housing. Confusion reigned. Couple that with the aftermarket dropping 4 series carriers in the Ford High pinion Dana 60, and the fact that the Dana 61 used Dana 60 gears with a D61 carrier, unless it was a Trac Lok, then they used D61 Gears with the D60 carrier. Nothing made sense after that.