I'd say a bar is somewhere you stand up, probably has music and would go in the evening and into the night. They're almost exclusively in towns/cities or in hotels.
You'll find pubs in the countryside as well as the city and you'd' be sitting down, are open in the daytime as well as evening and are more likely to serve food.
I wouldn't say that's an official definition, but that's how I think of them. Also, I'd say a bar is a bit smarter, and a pub more relaxed, but that's more of a blurry line to me.