Originally Posted by Kentishman
I could be laboring/labouring under a misapprehension, but I think the first link exhibits a 2/3 or 3/4, whatever fraction, lining and the second link exhibits a 'butterfly' shoulder lining.
A buggy lining has a French-faced partial front lining (the same fabric as the exterior) and a shoulder lining as that in the first link. The most common use of the term is in outerwear, most often in genuine Scottish Mackintosh long riding coats made by Traditional Weatherwear of Cumbernauld, Scotland, for instance. The back shoulder partial lining of such outerwear is usually of blanket weight wool in Tattersall or checked patterns. It can also be found in Palm Beach style (the style, not brand) odd jacket and suit linings, the 'buggy" shoulder lining being Bemberg.
Whence the name? Dunno, but suspect horsies, sodomites or creepy-crawlies are involved.