Prior to the British occupation of the Indian Contingent the Indian geographical boundaries comprised the entire Pakistan and even Afghanistan and the entire Khyber Pass through which Alexander The Great invaded Samarkhand and subsequently India.
Prior to the invasion of the Greeks the Iranian traders would venture in this territory for trade and the Alaunts would come along with them and they must have been there long before Alexander invades Samarkhand.
During the time Alexander the Great would conquer Samarkhand and fall in love with the Princess of Samarkhand, a lady of legendary beauty whom many thought as a myth. He got married to the Princess of Samarkhand, Rushnak, whom he called Roxanne, as he found difficult to pronounce the name Rushnak. Alexander’s brief stay in Samarkhand (now Part of Afghanistan) for more than usual time allocated in his plan. His Assyrian Mastiffs and the Medians (known for their fighting breed), and the Indian Mastiff originally being in this region, might have mated to create the great Gawii, the Afghanistani Bulldog.

A true type Bully Kutta called Dagger. Owned By Mr. Hammad Hassan from Pakistan.

During this time when Gawii is fading fast, a drop or two of Gawii’s blood found its way into the available Alaunt (or its version), creating a specimen which when crossed with the Indian Mastiff achieved a formidable size and temperament to become the Bully Kutta.
Bully survived being light footed and longer nosed with the tough Gawii temperament, and it gained much deserved popularity.

A fawn colored Bully Kutta owned by Hammad Hassan.

The entire Indian continent being a princely state was divided into many kingdoms and each had their own preferences. So the Bully Kutta survived in being different forms and shape as per the zonal preferences. This went far into the history and after Pakistan was created, each and every zone would have its own type of Bulldog, or populary called Bully. This is where the confusion began. The Area of Kohat has their own version of Kohati Bull dog, Sargodha has their own type and the Indian Mastiffs (otherwise called Sindh Mastiff) in the Sindh Area and in the Bhawalpur area of Punjab, will also be called the Bully as they all belonged to the Bull breed.
The Kohati Bull Dog is known for its excellent guarding and hunting abilities but loosing its popularity recently due to their lack of proper attitude required for fighting.

Different regional versions of Bully Kutta, which now breeds true to its types.
Photographs are used with permission from Adeeb Razzaq and Hammad Hassan.

With time, even crosses of Kooche Dog and Bully Kutta and even Tosa Bully mixes get accepted as Bully. It is a very confusing zone to locate a proper Bully Kutta. Buyers be aware, and do go to Pakistan for some research before buying a Bully Kutta, and watch the Bully kutta in its element and decide if you are capable of managing a dog and man aggressive dog as the Bully kutta in the first place.
However it is to be noted that every different versions had enough time to standardize and now breeds true to its type. But people living in the gray zone will exist everywhere and as long as the dog fights goes on these group of people will keep on experimenting and keep introducing various bull type mixes as Bully Kutta. This is how the Original Bully Kutta got lost.
However there are few (I mean very few) breeders in Pakistan and a couple in India who are breeding true Bully Kutta and try their best to keep them in their original shape and form. Mr. Hammad Hassan is one such Pakistani breeder who not only strives hard to breed Bully true to its type but also tries his best to restore the breed in its pristine form.

Pictures from Mr. Sagir Shah, which shows his brother and a Bully Kutta.