Except of course in that the milk had drugs added to it, while the point of the real milk bars was to provide a similar atmosphere to a pub without the intoxication.
The Pathé newsreel in the video embed at the bottom of the page explicitly states that milk is tasty "when you know how to drink it" while showing a man pouring almost certainly alcoholic liquor into the milk.
Proprietors of a soda fountain in Aspen, Colorado made the Aspen Crud, a cocktail of ice cream laced with bourbon, taking advantage of laws that enabled drugstores to sell alcohol for medicinal purposes.
Normally in a pub you have multiple drinks over the course of an hour or more while you socialize. It's a very different scene than restaurant where you order a meal, eat it, and leave. Cafes/coffee houses could be similar but still, while I have been known to drink several pints at a pub, I can't imagine drinking several lattes in sequence -- the caffeine would seem too much.
It's also in a lot of Nintendo games (or at least the US localizations), I always assumed it was something they made up as a cute kid-friendly alternative to having literal bars in their fictional worlds.
I had no idea this was actually a thing.