The list given is not exhaustive; it omits the configuration with a D on single regulator sets, which is not uncommon (i.e. the single reg is what we would now call a ‘baritone’); also not mentioned is the single regulator which plays only D, which I have seen on a couple of occasions.
A common union pipe combination which also shows up on Pastoral sets is the two-reg configuration with 3 and 4 keys, respectively - in effect, the modern 2 reg setup without the uppermost rank:
bari: G F# D
tenor: B A G F#
I have seen several cases where the D on the baritone was added, as a separate joint, to what would otherwise be considered a tenor. I have also encountered a couple of instruments where the D note was played by a stand-alone regulator, with a separate ‘tenor’ (to use today’s nomenclature). Taken together this suggests that the second regulator may have originated as a single note, ‘D’, from which it is only a small extrapolation to the ‘add on’ D joint and the presence of two multi-keyed regulators with some redundancy.
In the early days of both instruments, the two regulators were referred to as ‘unison’ and ‘pupilow’. There is some question as to which was which. If however you take the hypothesis that the following regulator configuration was one of the earliest:
D
B A G F#
then it makes sense that the D reg was the unison and the four-key regulator was the ‘pupilow’.
Thanks to (Dr.) Jimmy O’Brien-Moran, who did some digging in Italian dictionaries, one finds ‘pupilow’ an Italian word meaning, variously, ‘ward’, ‘pupil’, etc., a diminutive term suggestive an understudy or ‘person under protection’, from which we get the English word ‘pupil’. This aptly alludes to the relationship of the four-key regulator above to the chanter.
It also reflects the formal musical context of various pipe tutors of the day, where Italian was the language of ‘cultured’ European music.