So they are both pork based BBQ, distinct from brisket and other more "Texas" BBQ which is traditionally beef. Eastern BBQ is the whole hog being smoked normally while the western or "Lexington" style is the pork shoulder primarily. Eastern then uses a vinegar based sauce that is thinner than the normal expected BBQ sauce you'd find in the bottle at a store. The idea is the vinegar and spices in the eastern style stand to enhance the natural flavor of the meat with just a kick of spice. Western uses the more common idea of barbecue sauce that is tomato based, sweet, and sticky. These sauces normally have a more distinct flavor that is the goal moreso than the meat itself. I'm by no means a professional chef or food historian so this may not be 100% accurate but I hope it explains some! There is an interesting history behind the origins of each as well that I encourage a read on for fun!