Or, if you want the context of why the BJCP makes a distinction, read the comments in category 18E:
"Barleywine-type beers (e.g., Scaldis/Bush, La Trappe Quadrupel, Weyerbacher QUAD) and Spiced/Christmas-type beers (e.g., N’ice Chouffe, Affligem Nöel) should be entered in the Belgian Specialty Ale category (16E), not this category."
Basically, the BJCP calls the Trappist and Abbey style a Belgian Dark Strong, except for some rare outliers. Why do some of the American beers call themselves Quadrupel even though they fit in the Dark Strong category? Probably because they think the name is cool.