Bar is from the USA and a Pub is from the UK well to me anyway!! You have to dig a little further than to question!! What is a pub? it a Public House and what is a Public house? What is a Free house and what is a brewry tap???
Read "A Man Walks into the Pub" by Pete Brown - a fantastic book that covers the social history of beer. One of the chapters covers the differences between public houses, taverns, alehouses, beer houses, Inns, taprooms, and hotels. They all had different legal status (this is from a UK perspective admitedly - but that is the background to much of the usage in the english speaking world).
The differences in usage now are the result of habit and local tradition as many of the legal requirements are obselete and people are free to use the terms as they wish.
In NZ there is still a legal framework to the licensing but it doesn't affect what you chose to call the business. The Moutere Inn, legally, is in fact a tavern as that is a specific legal license - but we're free to use "pub', 'hotel', 'inn' or any other term in our trading name.