liquor in AB is no longer significantly cheaper than BC, with the exception of maybe some hard alcohol. Beer and Wine are pretty much a wash...
In fact, last time I was living in Alberta but regularly driving to BC a couple years ago, it was cheaper to buy most beers/wines in BC, and nearly the same on hard alcohol (mostly because of Costco liquor stores being available in AB but not BC).
Yes and No. They buy at Costco, which is cheaper than the liquor stores in their town. In BC only liquor stores can sell, whereas in AB grocery stores can as well. This can lead to grocery stores being cheaper than liquor stores.