One - maybe slightly meandering - consideration of mine. More tentative yet, than pontificating... ;-)
The Drilling in its classical and popular configuration was and is often touted as the "universal one-stop hunting weapon", with its shot barrels suited for all kinds of small game on feet or wings (an approximation only for the characteristic German term "Niederwild", which includes roe deer, but excludes capercaillie, eagle, and even the smallest piglets), and the rifle barrel for "Hochwild" (cannot be translated as big game).
The typical "Försterdrillling" in 16/65-16/65 (at times also 12/65) and 9,3x72R or 9,3x82R was considered the affordable and universally useful gun, more modern in its - tempi passati - "small-bore, flat-shooting rifle round" (ha-hah) than the older English-influenced straight express cases such as 11,15x65R and all so-called "Lancasterpatronen".
The double rifle Drilling would be considered a specialized and expensive weapon of discerning choice for the "Hochwildjäger" (today, nigh 100 % of all German hunters are by necessity Hochwildjäger now, since wild boars are nearly omnipresent), or for the African hunter. Still today, a few affluent hunters tote a DBD at driven game hunts, in the way of a double rifle.
Bockbüchsdrillinge are near extinct, since the small barrel's purpose today is nearly always fulfilled by inserts in one shot barrel.
(Vierlinge are a toy - an expensive toy for adult boys. You have it, fondle it, brag around and show off, but you do not really hunt with it)
What we have *here* in my auction link, however, would appear to be an unusual purpose - a "Niederwilddrilling":
Elegant, still reasonably lightweight, not meant for larger game. Shotgun size best for stylish woodcock. ;-)
Rifle barrel to be used for fox, badger, roe deer. A hundred years ago for capercaillie (as still today in Scandinavia and Finland).
Carcano
