The Double Four, or “44”, is the name given to the 7.92x33mm Kurz, the round first developed for the famous Sturmgewehr 44, manufactured by craftsman in the famous gun workshops of Darra Adam Khel, Pakistan and which are popular in Pakistan’s tribal regions.
Local lore says that the Double Four was introduced during early years of the Soviet war in Afghanistan in order to hide involvement of the CIA and Pakistan Intelligence who were supplying the Afghan Mujahedeen. While there is no way to verify if this story is true, we do know that the CIA went to extreme lengths to hide, or at least be able to plausibly deny, their involvement in shipping ammunition and weapons to Pakistan Intelligence who in turn distributed it to the Mujahedeen.
Post-CIA, I am not sure what the benefit of the slightly shorter round is in a full length rifle. The only benefit I can think of is that it may cost slightly less to manufacture. Most likely it is still popular because many rifles chambered for it are still floating around Pakistan. In the early 90s Colt developed the 5.56x30mm MARS and recently India developed the 5.56x30mm INSAS, but these were for use in compact PDW-style weapons not rifles.
This AK-style rifle above is designed to fire the Double Four. I was told that is can be quickly converted to fire regular 7.62x39mm ammunition if required. It uses standard 7.62x39mm AK magazines.
UPDATE: Turns out
Many thanks to Zain for the information and photos.