A tavern is a place where you can buy and drink an alcoholic drink; an inn is a place where you can you have a meal and spend the night. The terms are sometimes used interchangeably.
According to Encyclopaedia Britannica Online, a tavern is "an establishment where alcoholic beverages are sold for consumption on the premises. Tavern keeping has paralleled the growth of trade, travel, and industry throughout history and virtually worldwide."
Dictionary.com defines an inn as a commercial establishment providing, among other things, lodging and food for the public, particularly travelers. It also calls an inn a small hotel and gives "a tavern" as its secondary definition.
Tavern on the Green in Central Park, New York City, may be one of the most famous taverns in the United States, but it is more than a place to drink. The gaudily decorated restaurant has indoor and outdoor dining and multiple rooms for parties, weddings and other functions.
The word "inn" is often used interchangeably in the United States with the terms "bed and breakfast" and "B&B." The website for Inns in America lists inns and bed and breakfasts throughout the United States.
Janet Rodgers, in "The Innkeeper's Letter," writes, "an Inn is another word for a Bed & Breakfast." She goes on to say that having a restaurant or pub open to the public makes a bed and breakfast into an inn.