To me, BYOB means bring your own booze. 
No two ways about it around here, and I'd expect there'd be punch, iced tea (unsweetened, this is New England, what is this 'sweet tea' of which you speak?- jk!), juice pouches/Capri Sun (if there are kids invited), lemonade, soda, SOMETHING to drink (not necessarily all, but some, of these).
When I was growing up, BYOB meant "Bring your own bottle," but it was clearly understood that "bottle" meant liquor/alcohol. Parties that were byob provided "soft" drinks and beer, even. My parent's circle of friends were very clear on that- "bottle" meant "bottle of booze." I still understand "BYOB" means to bring your own alcohol, if you wish to imbibe, but that non-alcoholic drinks will be provided. If this is NOT the case, the invitation often says "BYOBeverage."
We always have brought our own everything, anyhow. DD doesn't drink soda at all, if I am drinking soda I want DIET soda, and if DH and I are drinking beer, we DON"T want Old Milwaukee! Of course, we've also been known to bring along a jug of sangria or margaritas!
