The confusion arises because the type of VA that was common before brightleaf was air or fire cured brown VA or Orinoco. This leaf was given up on by most US farmers in favor of brightleaf long ago. Some manufacturers like MacBaren refer to this leaf, either mistakenly or because they feel it makes more sense to the consumer, as burley. Gawith and other UK producers refer to it as dark VA or Brown VA, or fire/air cured VA.
The old style of Dark KY, both air and fire cured is closer to the original burley, but when most Americans (and, I presume, Europeans) hear burley they think of "white" or light burley, which is a mutated variety of burley that is spongy, pale, very low in sugar, and, most importantly, soaks up casings better than any other variety. It became popular as a cigarette filler because it soaks up additives so well, and eventually became the most popular tobacco for OTCs and cheap cigars because it's so easy to flavor... and because it's a cheap filler by nature.
The English and Dutch had their colonies growing tobacco for them, and these regions have continued growing the older, bolder style of brown VA because the locals prefer it, and because they are the only suppliers to the euro market.
The story is often recounted that oriental tobacco seeds were brought to the US, but after a generation they just looked and tasted like burley. I believe they are just regionally adapted brown VA, but saying they taste like burley is the easiest way to describe without having to go through the history of cultivated VA like I just did?
As a side note, they are now growing Orinoco on George Washington's estate (as he did). I have a suspicion that Maryland leaf is also an offshoot of this Orinoco, as it's often described as having low sugar and a flavor similar to Ky, but the thin leaf structure of VA.
I would describe African and Mysore dark VA as tasting a bit like a cigar wrapper, but with as much variation due to curing methods and growing region as cigar leaf, so that's a fairly wide descriptor.