Yeah, down here we say grilling if that's what we are doing- i.e. burgers, hot dogs, etc. We say
barbecue if we are smoking some meat or having such things like pulled pork, ribs, etc. When I was a kid visiting my datd in RI I was told we were going to a barbecue - I was shocked to find that there was no barbecue actually there, only beurgers and dogs. Reminds me of this: