Well I have a pub table & it's different from a normal table in that it sits very high, as does it's chairs. Presumably so you can stand there & chat with those sitting at it without them having to look at your crotch or you having to bend over to pick up your drink.
I don't have a breakfast bar but I imagine it sits lower as other tables for eating.

A pub table standard height is 36" high and requires a 30" stool. A breakfast bar can be 30" high, like a standard table or counter height which again is normally 36" high.