I think maybe the terms used are different, but if the bar is a business owned by a private person or company, and is allowed to say who can be in there or not, set dress code, hours, rules about outside food etc, that's what would be considered a place of business in the US, and those aren't publicly-owned or considered a public space as far as the rights of those people in that space. I get that "pub" literally means "public" but they aren't owned by some government entity, you don't have a "right" to free access to them, and the rules about what can and can't take place there are set by the private owners.