Are you looking for a musket or a fowling piece?
Both are smoothbores but a musket is a millitary arm while a fowling piece is a sporting arm designed to hunt fowl, i.e. a shotgun. A musket can certainly be used as a fowling piece however.
The most well known muskets are the Tower musket also known as the "Brown Bess" used by the Redcoats and also a lot of the Continental army. This is a .75 caliber smoothbore (11 gauge), and the French Charleville musket which was .69 caliber (14 gauge) and used by the Americans because the French were kind of on our side in the war.
There is another class of smoothbores known as "trade guns" which were built to be traded to the Indians. These were typically 20 gauge.
Also, there was a catagory of smoothbores that are commonly referred to as "smooth rifles" these had rifle style rear sights and were made in rifle calibers. Some folks felt that rifling was over-rated and preferred the easy cleaning and versitility of a smoothbore.