Larry has stated this very well.
Note the following points though. If a bbl has a 16ga chamber & a .637" bore we would call it a 16ga gun, But, it technically does not have a 16ga bore. It has an 18ga bore. As defined gauge of a shotgun is a measurement based on the weight of a pure lead round ball. It is as such a given size & not a "Range" of sizes at all. The technically correct size for 16ga is .662", period.
This of course does not guarantee what any maker may have bored a bbl to.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra