Balkans?

I think my brain just pooped 8O

It is a marketing term and there are no legal guidelines so it means whatever its blenders want it to mean...
Go on a beer forum and ask the question: what is the difference between porter and stout?
If you want to pick nits, there is no major difference - producers, however, have created a distinction between the two in the minds of consumers in recent years and that is significant to my mind.
Whether it is accurate or not is anyone's guess, but I personally consider a Balkan to be a heavy latakia blend with an emphasis on orientals and with Virginias in the background.
I consider English blends, however, to have a greater percentage of Virginias, a mild to moderate level of latakia, no-low-medium orientals, and occasionally other condimental tobaccos such as cavendish or perique.
Sure, there are plenty of exceptions, but this is what I think about when these terms come up...
Long story short - English blends and Balkan blends are brothers, if not fraternal twins.

They are English blends that put the Virginia far in the background, bringing the Latakia and orientals to the foreground. (To my mind, these are the essential -- and only -- tobaccos that should be present in a true Balkan, but that's a personal judgment.) Different Balkans will rely on different kinds of orientals for this; some are a bit acrid, while others are richer and smoother. All have their place. But for me the best Balkans are the ones in which the Latakia and orientals come together in such a way that the aroma and mouth feel become creamy. It's a flavor experience I've never encountered with anything but a Balkan blend.
GLPease is the only blender offering a range of Balkans, which includes Ashbury, Kensington, Charing Cross, Caravan, and Odyssey. But another excellent one is McClelland's Grand Orientals: Yenidje Highlander. It isn't marketed as a Balkan, but it's a Balkan in the tin.
Some do also add perique to the mix, which I can't smoke and can't comment on. Black House bills itself as a Balkan, but for me the presence of a good bit of burley in that blend throws it completely off.

Balkans are blends that resemble the original Balkan Sobranie smoking mixture. Which in turns means roughly: Lots of Latakia, and then Virginia and Orientals to balance. As Oriental variety most blends use Turkish, i.e., Yenidje.
There are also Oriental Blends, that mainly use an Oriental variety like Yenidje, Samsun, Xanthi, Smyrna or Shirazzi, sweeten it with Virginia and balance it out with a touch of Latakia.
I thinks the distinction is more about the relative amount of ingredients to each other, than the exact ingredients, for example,
English: Virginia and Latakia about equal, a pinch oriental for the palate. ("burning rubber")

Balkan: Latakia foremost, then Virginia and Orientals about equal. ("spicy burning rubber with licorice")

Oriental: Oriental tobaccos take the main spot, balanced out with a bit Virginia, a pinch Latakia for the palate. ("Herbal, buttery, a bit spicy, someone burned rubber there a week or so ago ...")

Balkans are blends that resemble the original Balkan Sobranie smoking mixture.

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I'm curious why you say this. I think Sobranie chose to call this blend "Balkan" because that's what it is. I don't believe they invented the style. But if they did, I'd love to know where that's documented.
BTW, I didn't mention the reborn Balkan Sasieni in my list above. That's because I have serious reservations about it. First, it is suspiciously cheap. Second, after smoking a tin, I am convinced that this blend has supplemented its oriental tobacco with oriental flavoring; every single bowl I've smoked saw the oriental component vanish from the bowl by the halfway point. Real tobacco doesn't do that consistently from bowl to bowl. I may be wrong. But it helps to explain the pricing -- as well as my actual experience.