A commonwealth and a state are exactly the same thing; the term "commonwealth" was originally used to indicate that a particular region was not governed by a monarch but by the people. There are four states that call themselves commonwealths: Kentucky, Pennsylvania, Massachusetts and Virginia.
The colonies of Pennsylvania, Massachusetts and Virginia declared their statuses as commonwealths during the American Revolution. Kentucky, at the time, was a part of Colonial Virginia. When Kentucky and Virginia separated in 1790, the term "commonwealth" was retained by the state. Notably, the Northern Mariana Islands and Puerto Rico, both U.S. territories, are also referred to as commonwealths.