The American barbecue sandwich, once it leaves the barbecue belt and turns up in London, Tokyo, Seoul, or Sydney, is defined by the one thing that does not travel: the smoker. Everything else can be shipped, sourced, or approximated, but a sandwich whose entire identity was built hours before assembly, over wood, depends on a pit and a pitmaster being on site. The export version is therefore a question of how faithfully the smoke can be reproduced far from where the style was set, and that question is the sandwich.
The craft abroad is mostly a sourcing and equipment problem. Texas-style brisket needs a packer cut held until the fat renders and the meat slices without falling apart, which means an offset smoker or a competent imitation of one and the patience to run it long. Carolina pulled pork needs a shoulder taken to the point where it shreds into bark and tender interior, then dressed with a thin vinegar sauce that an export kitchen often has to make rather than buy. Kansas City burnt ends need the brisket point cubed and returned to the smoke to render and bark a second time. The bun stays deliberately plain wherever the sandwich lands, because the rule that the bread should disappear under the meat does not change with the country. What changes is the slaw and the sauce: the local market decides whether the cabbage goes on for crunch and acid, and regional sauce arguments that are settled by geography at home become a menu choice abroad.
The variations are the regional American styles themselves, now scattered across cities that never had a dog in the original fight. A Tokyo counter may run a Texas brisket build with a tighter, sweeter glaze; a Seoul kitchen may push the pulled pork toward a gochujang-inflected sauce; a London room may serve all three styles side by side and let the eater pick the argument. Each of those source styles, Texas brisket, Carolina whole hog and shoulder, Kansas City burnt ends, is its own discipline with its own rules and deserves a proper article rather than being crowded in here.