Actually, there is correct and there is incorrect, and just because you grew up using it incorrectly doesn't make it defacto correct. For example, it's normal around here to use double negatives to mean a negative. Doesn't make it correct; bad english and bad logic is just that. Luckily we know what is the intent, normally.
For example, there are automobiles, which have a few types, like cars, and trucks, SUV's, and motorcycles, and a few others. Within trucks you might have the Ford F150 and F250, the Chevy 1500 and 2500. If you were intending to test drive the Ford F150, you wouldn't say "I'm going to look for a car". You're looking a trucks. They're both automobiles, but they're NOT the same.
There's cooking. In cooking styles (there are MANY), there's grilling, barbecuing, frying, baking, and many others. They mean different things. If you're putting that steak on the weber over direct heat at probably 500 degrees, you're definitely grilling, not BBQ'ing. You can however put a boston butt on that weber, usually moving the coals to the side, run it at about 275 degrees and while you're using the same equipment, you're BBQing not grilling.
That's why if you're having a shin-dig outside, we just say correctly "cook out", which could be grilling (most of the time does), or could mean bbqing. However, if you say "we're having a bbq", it actually means you'll be barbecuing something, when in fact most people are wrong, because they're grilling...
I'm not about to tell you to stop or correct you. That's fine. It would be like trying to get the folks from Lizella GA to stop using the double negatives; wont happen and only will piss everyone off... But, it doesn't make it correct.
Side note: I loved it when my brother first looked at my Lang and said "Holy cow, how many steaks can you grill on that?", and I politely answered "None. It doesn't grill. The baffle runs right under the grate, so it's strictly a BBQ machine".