This is kind of funny. Recently we received a wedding party invite that said something like, "join us for some beer, bbq, and fun."
When we arrived, it was hot dogs, hamburgers, potato chips, etc.
One of the other guests pulled me aside and said that they felt misled by the "BBQ" in the invite and that, had they known it was going to be grilled burgers & hotdogs, they wouldn't have given such a generous "gift".
I guess it really never occurred to me until then but some people have different expectations when they hear BBQ.
For me personally, I use BBQ as a general term much like the phrase, "cook out".
In my experience, the terminology is VERY localized.
English is a messy language compared to some others and is always changing, but not as bad as German was in the old days...but I digress.
In the end it comes down to local terminology and customs.
For example, I currently live on the plains. Here BBQ generally means a fire with smoke. While grilling can have many meanings including in a skillet on the electric stove top (think "grilled cheese").