Actually….to get picky its all about the way you use it not the bbq/hob it self.
Bbqing is actually more like oven cooking, cooking for a long time on a low heat – perfect for ribs, whole chicken etc, usually using wood chips to enhance the flavour. This is rarely done in the UK. Grilling is the usual way here, cooking relatively fast on a high heat, cooking burgers, sausages etc etc. Often the way they do it in SA and Oz too, while bbqing is African, Caribbean and American style.
A BBQ can usually grill while its a lot harder to BBQ on a grill.