"Bar" is certainly the catch-all term in the U.S., but "pub" is also very widely understood to refer to a specific type of bar, especially (but not limited to) bars deliberately styled as Irish or British pubs.
every now and then you'll find a public house or similarly named
Along a similar note, I hate when a Bar is labelled as a "Pub" and doesn't serve food. IMO, in the US, if it's labelled a "pub" it should serve food.