"To the best of my knowledge there really isn't one. It is a historical naming issue. In the early days of colonization, commonwealth was practically synonymous with 'republic' or 'state'. Some preferred the term because they liked the implied meaning better. But I do not believe there is any meningful distinction that differentiates a commonwealth from a state.However, in modern parlance, there
. is a tendency to use the term commonwealth to refer to a government with local autonomy but which is a protectorate of some other nation as is the case with US held territories like Puerto Rico. However this modern spin on the word should not be taken as implying any legal distinction between US states which are commonwealths vs states that are not."